# Factors of 72 in pair

Factors of 72 in pair are (1, 72) , (2, 36) , (3, 24) , (4, 18) , (6, 12) and (8, 9)

#### How to find factors of a number in pair

 1.   Steps to find factors of 72 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 72 in pair

Factor Pair Pair Factorization
1 and 72 1 x 72 = 72
2 and 36 2 x 36 = 72
3 and 24 3 x 24 = 72
4 and 18 4 x 18 = 72
6 and 12 6 x 12 = 72
8 and 9 8 x 9 = 72

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 72. They are called negative pair factors.

Hence, the negative pairs of 72 would be ( -1 , -72 ) .

#### How do you define factor pairs of a number?

A factor pair of a number can be defined as the combination of two factors in such a way that when multiplied together produce the number itself. Every natural number is a product of atleast one factor pair. Eg- Factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72. So, factors of 72 in pair are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9).

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 72 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 72.
• Every number is a factor of zero (0), since 72 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are exact divisors of 72.
• Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Each factor divides 72 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 are all less than or equal to 72.

#### Steps to find Factors of 72

• Step 1. Find all the numbers that would divide 72 without leaving any remainder. Starting with the number 1 upto 36 (half of 72). The number 1 and the number itself are always factors of the given number.
72 ÷ 1 : Remainder = 0
72 ÷ 2 : Remainder = 0
72 ÷ 3 : Remainder = 0
72 ÷ 4 : Remainder = 0
72 ÷ 6 : Remainder = 0
72 ÷ 8 : Remainder = 0
72 ÷ 9 : Remainder = 0
72 ÷ 12 : Remainder = 0
72 ÷ 18 : Remainder = 0
72 ÷ 24 : Remainder = 0
72 ÷ 36 : Remainder = 0
72 ÷ 72 : Remainder = 0

Hence, Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72

• Is 72 a composite number?

Yes 72 is a composite number.

• Is 72 a prime number?

No 72 is not a prime number.

• What is the mean of factors of 72?

Factors of 72 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 18 , 24 , 36 , 72. therefore mean of factors of 72 is (1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 36 + 72) / 12 = 16.25.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Ariel has been asked to write all factor pairs of 72 but she is finding it difficult. Can you help her find out?

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. So, factors of 72 in pair are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9).

Sammy wants to write all the negative factors of 72 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 72 are -1, -2, -3, -4, -6, -8, -9, -12, -18, -24, -36, -72. Hence, factors of 72 in pair are (-1,-72), (-2,-36), (-3,-24), (-4,-18), (-6,-12), (-8,-9).

Help Deep in writing the positive factors of 72 in pair and negative factor of 72 in pair.

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Positive factors of 72 in pair are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9). Negative factors of 72 in pair are (-1,-72), (-2,-36), (-3,-24), (-4,-18), (-6,-12), (-8,-9).

Find the product of all factors of 72.

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. So the product of all factors of 72 would be 1 x 2 x 3 x 4 x 6 x 8 x 9 x 12 x 18 x 24 x 36 x 72 = 139314069504.

Find the product of all prime factors of 72.

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Prime factors are 2, 2, 2, 3, 3. So, the product of all prime factors of 72 would be 2 x 2 x 2 x 3 x 3 = 72.

Can you help Sammy list the factors of 72 and also find the factor pairs?

Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Factors of 72 in pair are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9).

Sammy has 72 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 72 blocks in all possible ways to form a rectangle, we need to calculate factors of 72 in pair. Therefore, factors of 72 in pair are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9)