# Factors of 144 in pair

Factors of 144 in pair are (1, 144) , (2, 72) , (3, 48) , (4, 36) , (6, 24) , (8, 18) , (9, 16) and (12, 12)

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

 1.   Steps to find factors of 144 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 144 in pair

Factor Pair Pair Factorization
1 and 144 1 x 144 = 144
2 and 72 2 x 72 = 144
3 and 48 3 x 48 = 144
4 and 36 4 x 36 = 144
6 and 24 6 x 24 = 144
8 and 18 8 x 18 = 144
9 and 16 9 x 16 = 144
12 and 12 12 x 12 = 144

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 144. They are called negative pair factors.

Hence, the negative pairs of 144 would be ( -1 , -144 ) .

#### What does factor pairs of a number mean?

Factor pairs are those factors in pair that can give original number when multiplied. Every natural number is a product of atleast one factor pair. Eg- Factors of 144 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 16 , 18 , 24 , 36 , 48 , 72 , 144. So, factors of 144 in pair are (1,144), (2,72), (3,48), (4,36), (6,24), (8,18), (9,16), (12,12).

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 144 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 144.
• Every number is a factor of zero (0), since 144 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, 16, 18, 24, 36, 48, 72, 144 are exact divisors of 144.
• Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Each factor divides 144 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, 16, 18, 24, 36, 48, 72, 144 are all less than or equal to 144.

#### Steps to find Factors of 144

• Step 1. Find all the numbers that would divide 144 without leaving any remainder. Starting with the number 1 upto 72 (half of 144). The number 1 and the number itself are always factors of the given number.
144 ÷ 1 : Remainder = 0
144 ÷ 2 : Remainder = 0
144 ÷ 3 : Remainder = 0
144 ÷ 4 : Remainder = 0
144 ÷ 6 : Remainder = 0
144 ÷ 8 : Remainder = 0
144 ÷ 9 : Remainder = 0
144 ÷ 12 : Remainder = 0
144 ÷ 16 : Remainder = 0
144 ÷ 18 : Remainder = 0
144 ÷ 24 : Remainder = 0
144 ÷ 36 : Remainder = 0
144 ÷ 48 : Remainder = 0
144 ÷ 72 : Remainder = 0
144 ÷ 144 : Remainder = 0

Hence, Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144

• Is 144 a composite number?

Yes 144 is a composite number.

• Is 144 a prime number?

No 144 is not a prime number.

• What is the mean of factors of 144?

Factors of 144 are 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 16 , 18 , 24 , 36 , 48 , 72 , 144. therefore mean of factors of 144 is (1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 36 + 48 + 72 + 144) / 15 = 26.87.

• 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 144 but she is finding it difficult. Can you help her find out?

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. So, factors of 144 in pair are (1,144), (2,72), (3,48), (4,36), (6,24), (8,18), (9,16), (12,12).

Sammy wants to write all the negative factors of 144 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 144 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144. Hence, factors of 144 in pair are (-1,-144), (-2,-72), (-3,-48), (-4,-36), (-6,-24), (-8,-18), (-9,-16), (-12,-12).

Help Deep in writing the positive factors of 144 in pair and negative factor of 144 in pair.

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Positive factors of 144 in pair are (1,144), (2,72), (3,48), (4,36), (6,24), (8,18), (9,16), (12,12). Negative factors of 144 in pair are (-1,-144), (-2,-72), (-3,-48), (-4,-36), (-6,-24), (-8,-18), (-9,-16), (-12,-12).

Find the product of all factors of 144.

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. So the product of all factors of 144 would be 1 x 2 x 3 x 4 x 6 x 8 x 9 x 12 x 16 x 18 x 24 x 36 x 48 x 72 x 144 = 15407021574586368.

Find the product of all prime factors of 144.

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Prime factors are 2, 2, 2, 2, 3, 3. So, the product of all prime factors of 144 would be 2 x 2 x 2 x 2 x 3 x 3 = 144.

Can you help Sammy list the factors of 144 and also find the factor pairs?

Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Factors of 144 in pair are (1,144), (2,72), (3,48), (4,36), (6,24), (8,18), (9,16), (12,12).

Sammy has 144 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 144 blocks in all possible ways to form a rectangle, we need to calculate factors of 144 in pair. Therefore, factors of 144 in pair are (1,144), (2,72), (3,48), (4,36), (6,24), (8,18), (9,16), (12,12)