What 2 Numbers Multiply To Get 72: Find The Pairs!

We can find several pairs of numbers that multiply to equal 72. Here are a few examples:

36 multiplied by 2 equals 72.
24 multiplied by 3 equals 72.
18 multiplied by 4 equals 72.
12 multiplied by 6 equals 72.
9 multiplied by 8 equals 72.

While it’s true that 2 and 3 are prime numbers (meaning they are only divisible by 1 and themselves), this doesn’t directly tell us how to get 72 by multiplying only prime numbers.

To get to 72 using only prime numbers, we need to consider the prime factorization of 72. This means breaking down 72 into its prime factors, which are the prime numbers that multiply together to give us 72.

Here’s the prime factorization of 72:

72 = 2 x 2 x 2 x 3 x 3

We can see that 72 is made up of three 2s and two 3s. So, to get 72 using only prime numbers, we can multiply these prime factors together:

2 x 2 x 2 x 3 x 3 = 72

However, the prompt asks for two numbers, not necessarily prime numbers. Therefore, the solutions presented at the beginning of this response are all valid as well!

Let’s explore multiples of 72!

The first 10 multiples of 72 are: 72, 144, 216, 288, 360, 432, 504, 576, 648, and 720.

You might be wondering, “How do I find these multiples?” It’s pretty simple! A multiple of a number is the result of multiplying that number by an integer.

For example, to find the first five multiples of 72, we multiply 72 by the integers 1, 2, 3, 4, and 5:

* 72 x 1 = 72
* 72 x 2 = 144
* 72 x 3 = 216
* 72 x 4 = 288
* 72 x 5 = 360

As you can see, each of these results is a multiple of 72. You can keep going to find more multiples by multiplying 72 by other integers.

You can also think about multiples of 72 in terms of their factors. Every multiple of 72 has 72 as one of its factors. For example, the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. Notice that 72 is a factor of 144.

Understanding multiples can be useful in a variety of situations, such as when solving math problems or when working with measurements. For example, if you are building a fence and you need to use 72-inch long planks of wood, you can use multiples of 72 to calculate how many planks you will need.

We’re looking for two numbers that multiply to 72 and add to 17. This is a simple system of equations that can be solved by a little bit of trial and error. The numbers we are looking for are 8 and 9, because 8 * 9 = 72 and 8 + 9 = 17.

Sometimes it can be helpful to use a more formal approach to solve these types of problems. One way to do this is by using the following steps:

1. Set up the equations: Let’s call the two numbers *x* and *y*. We know that *x* * y* = 72 and *x* + *y* = 17.
2. Solve for one variable: We can solve the second equation for *x*: *x* = 17 – *y*.
3. Substitute: Now we can substitute this value of *x* into the first equation: (17 – *y*) * *y* = 72.
4. Simplify and solve for y: Expanding the equation, we get 17*y – *y*² = 72. Rearranging this into a quadratic equation, we get *y*² – 17*y + 72 = 0. Factoring the equation gives us (*y* – 8)(*y* – 9) = 0. Therefore, *y* = 8 or *y* = 9.
5. Solve for x: We can substitute these values of *y* back into the equation *x* = 17 – *y* to find the corresponding values of *x*. If *y* = 8, then *x* = 17 – 8 = 9. If *y* = 9, then *x* = 17 – 9 = 8.

So we see that no matter which way we solve this, we always get the same answer: the two numbers are 8 and 9.

Yes, 72 is a multiple of 12.

Let’s break down why:

Multiples are the numbers you get when you multiply a number by a whole number (1, 2, 3, 4, and so on).
12 multiplied by 6 equals 72.

So, 72 is a multiple of 12 because it can be obtained by multiplying 12 by a whole number (in this case, 6).

Let’s explore the concept of multiples a bit further.

Think of multiples as a set of numbers that are all evenly divisible by a specific number, called the “base” number. For example, when we talk about multiples of 12, we’re looking for numbers that can be divided by 12 without leaving a remainder. This means that 72 is one of these numbers. We can find other multiples of 12 by multiplying it by different whole numbers.

Here are some examples:

12 x 1 = 12
12 x 2 = 24
12 x 3 = 36
12 x 4 = 48
12 x 5 = 60
12 x 6 = 72
12 x 7 = 84
12 x 8 = 96

And so on. We can keep multiplying 12 by larger and larger whole numbers to find an endless list of its multiples.

You’re asking how many times 72 goes into 2. This is a bit like asking how many times a large truck can fit into a tiny car – it just doesn’t work that way!

72 is a much larger number than 2. When we divide a smaller number by a larger number, the result is a fraction or a decimal. In this case, 2 divided by 72 is approximately 0.0278.

Here’s another way to think about it: Imagine you have 2 apples, and you want to divide them into groups of 72. You wouldn’t be able to create any full groups, you’d just have two tiny pieces!

Let’s break down what it means to divide a number:

Division is the process of splitting a number into equal parts.
* When you divide a number by another number, you’re essentially asking “how many times does the second number fit into the first number?”.

For example, if we divide 12 by 3, we are asking “how many times does 3 fit into 12?”. The answer is 4, because 3 fits into 12 four times (3 + 3 + 3 + 3 = 12).

In your case, 72 is much larger than 2, so it doesn’t fit into 2 even once. This means that the result of dividing 2 by 72 is a small fraction or decimal, indicating that 72 doesn’t go into 2 a whole number of times.

We can find out what number multiplied by 8 equals 72 by using division. We divide 72 by 8 and get 9.

9 multiplied by 8 equals 72.

You can think about it this way:

* Imagine you have 72 cookies. You want to divide them evenly into 8 groups. Each group would have 9 cookies.
* 8 groups with 9 cookies each would give you a total of 72 cookies.
* This is the same as saying 8 multiplied by 9 equals 72.

The key to understanding this concept is recognizing the relationship between multiplication and division. They are inverse operations, which means they undo each other. When we multiply a number by another number and then divide the product by the same number, we get back our original number.

This is a fundamental concept in mathematics, and it can be applied to many different situations. For example, if you know the area of a rectangle and one of its sides, you can use division to find the length of the other side. Similarly, if you know the distance you traveled and the time it took, you can use division to calculate your speed.

We can find half of 72 by dividing it by 2. When we divide 72 by 2, we get 36. This means that 36 is half of 72.

Let’s break down the division process further. In long division, we set up the problem with 72 as the dividend (the number being divided) and 2 as the divisor (the number we’re dividing by). We ask ourselves, “How many times does 2 go into 7?” It goes in 3 times. We write the 3 above the 7 in the quotient (the answer). Then, we multiply 3 by 2, which equals 6. We write the 6 below the 7. We subtract 6 from 7, leaving us with 1. We bring down the 2 from the dividend. Now, we have 12. We ask ourselves, “How many times does 2 go into 12?” It goes in 6 times. We write the 6 next to the 3 in the quotient. We multiply 6 by 2, which equals 12. We write 12 below the 12. We subtract 12 from 12, leaving us with 0. Since there’s nothing left to bring down, we’re done. Our final answer, the quotient, is 36.

So, dividing 72 by 2 means we’re splitting 72 into two equal parts. Each part is equal to 36. This is what we mean when we say “half of 72.”

Yes, 72 is a multiple of 8.

You can find out if a number is a multiple of another number by dividing the first number by the second. If the result is a whole number, then the first number is a multiple of the second. In this case, 72 divided by 8 equals 9, which is a whole number. This means 72 is a multiple of 8.

Let’s explore the concept of multiples a bit further. A multiple is a number that you get when you multiply a specific number by an integer. 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, and so on are all multiples of 8 because they are the results of multiplying 8 by different integers. For example:

8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
* … and so on.

You can continue this pattern to find all the multiples of 8.

Here’s a simple way to think about it: multiples are like groups of things. If you have a group of 8 apples, then 16 apples would be two groups of 8, 24 apples would be three groups of 8, and so on. Each group represents a multiple of 8.

Let’s break down how to find the factors of 72 using multiplication.

Step 1: Finding the Pairs

To find the factors of 72, we need to figure out which pairs of numbers multiply together to equal 72. We’ll start by dividing 72 by natural numbers, beginning with 1. We’ll keep going until we hit 9. Any number that divides 72 evenly is a factor.

Step 2: Identifying the Factors

The numbers that divide 72 completely are its factors.

Here’s how we can find them:

1 x 72 = 72 So, 1 and 72 are factors of 72.
2 x 36 = 72 So, 2 and 36 are factors of 72.
3 x 24 = 72 So, 3 and 24 are factors of 72.
4 x 18 = 72 So, 4 and 18 are factors of 72.
6 x 12 = 72 So, 6 and 12 are factors of 72.
8 x 9 = 72 So, 8 and 9 are factors of 72.

Important Note: We stop at 9 because the next number in our sequence (10) is larger than 9, and we’ve already found all the pairs of factors.

Let’s Recap:

We’ve now identified all the pairs of factors for 72. They are:

* 1 and 72
* 2 and 36
* 3 and 24
* 4 and 18
* 6 and 12
* 8 and 9

Remember, factors are numbers that divide evenly into a given number. In this case, we’ve used multiplication to find all the factors of 72.

Let’s break down how to calculate 72 / 2. It’s a simple division problem, but understanding the steps can be helpful.

Step 1: Start by dividing 72 by its smallest prime factor, which is 2. This means we’re figuring out how many times 2 goes into 72. The answer is 36.

Step 2: We’ve successfully divided 72 by 2 once. Now, we need to see if we can divide the result, 36, by 2 again. Since 36 is divisible by 2, we do so, and 36 / 2 = 18.

Step 3: We can continue dividing the result by 2 as long as the result is divisible by 2. In this case, 18 is divisible by 2, so we have 18 / 2 = 9.

Step 4: We’ve now divided the original number, 72, by 2 three times. The current result, 9, is not divisible by 2. This means we’ve reached a point where we can’t divide by 2 anymore.

Important Note: A prime factor is a number that can only be divided by itself and 1. The prime factorization of a number is a list of all its prime factors. For example, the prime factorization of 72 is 2 x 2 x 2 x 3 x 3, because these are the only prime numbers that can be multiplied together to get 72.

Let’s break down the factors of 72. Factors are numbers that divide evenly into another number. Since 72 is a composite number, it has multiple factors besides 1 and itself.

Here are the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

You can think of factors as pairs of numbers that multiply together to give you the original number. For example:

* 1 x 72 = 72
* 2 x 36 = 72
* 3 x 24 = 72
* 4 x 18 = 72
* 6 x 12 = 72
* 8 x 9 = 72

There are also prime factors, which are prime numbers that divide into a given number. Prime numbers are numbers greater than 1 that can only be divided evenly by 1 and themselves (e.g., 2, 3, 5, 7, 11, 13…).

To find the prime factors of 72, you can use a factor tree:

1. Start by dividing 72 by 2, which gives you 36.
2. Divide 36 by 2 again, which gives you 18.
3. Continue dividing by 2 until you get 9.
4. Since 9 is not divisible by 2, divide it by 3, which gives you 3.
5. Finally, divide 3 by 3, which gives you 1.

You’ve now factored 72 down to its prime factors: 2 x 2 x 2 x 3 x 3. You can write this as 2³ x 3².

Understanding factors and prime factors can be helpful in many areas of mathematics, such as simplifying fractions, finding the greatest common factor (GCF), and determining the least common multiple (LCM).

Let’s explore ways to find numbers that multiply to get 72!

You’re right, 36 and 2 multiply to get 72. But there are actually many other pairs of numbers that do the same!

Here’s why:

Factoring: Finding numbers that multiply to a target number is called factoring. It’s like breaking down a number into smaller pieces.
Multiple Pairs: 72 has several factors. Besides 36 and 2, you could also use 9 and 8, 12 and 6, or 18 and 4.
Beyond Whole Numbers: And there are even more possibilities if we include decimals or fractions! For example, 72 and 1 also work.

Finding Factors:

To find factors of a number, you can start by listing out its divisors. A divisor is a number that divides evenly into another number.

Here’s how you might find the factors of 72:

1. Start with 1 and 72: These are always factors of any number.
2. Check for divisibility by 2, 3, 4, and so on: Does 72 divide evenly by 2? Yes, it gives us 36. So 2 and 36 are factors.
3. Keep going: Does 72 divide evenly by 3? Yes, it gives us 24. So 3 and 24 are factors.
4. Continue until you’ve found all the pairs: You’ll notice that once you get to a factor that’s larger than its corresponding pair, you’ve found all the factors.

Having trouble finding factors? Don’t worry! There are online calculators and tools that can help you factor any number quickly.

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