What are the factor pairs of 72?

Understand the Problem

The question is asking us to identify all the pairs of factors that, when multiplied together, give the product of 72. We will methodically determine the pairs by finding the factors of 72.

Answer

The pairs of factors of 72 are \( (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9) \).

Steps to Solve

Identify the factors of 72

To find the pairs of factors, we first need to determine all the factors of the number 72. Factors are numbers that divide evenly into another number.

We can start checking from 1 up to the square root of 72 (which is approximately 8.49). The factors of 72 include:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Pair the factors

Next, we will pair these factors so that their product equals 72. We pair each factor with its corresponding factor that, when multiplied together, yields 72.

Here are the pairs:

( (1, 72) )
( (2, 36) )
( (3, 24) )
( (4, 18) )
( (6, 12) )
( (8, 9) )

List the pairs of factors

Finally, we list all identified factor pairs:

The pairs of factors that multiply to give 72 are:

( (1, 72) )
( (2, 36) )
( (3, 24) )
( (4, 18) )
( (6, 12) )
( (8, 9) )

The pairs of factors of 72 are ( (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9) ).

More Information

The number 72 is known as a composite number because it has more divisors than just 1 and itself. In multiplication, these factor pairs illustrate how different combinations can result in the same product.

Tips

Some may overlook certain factors or pairs. Always ensure to check all potential numbers up to the square root of the target number.
Forgetting to consider both orders of the factor pairs can lead to incomplete solutions. Each pair is distinct regardless of the order.

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