# Factors of 90 in pair

Factors of 90 in pair are (1, 90) , (2, 45) , (3, 30) , (5, 18) , (6, 15) and (9, 10)

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

 1.   Steps to find factors of 90 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 90 in pair

Factor Pair Pair Factorization
1 and 90 1 x 90 = 90
2 and 45 2 x 45 = 90
3 and 30 3 x 30 = 90
5 and 18 5 x 18 = 90
6 and 15 6 x 15 = 90
9 and 10 9 x 10 = 90

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 90. They are called negative pair factors.

Hence, the negative pairs of 90 would be ( -1 , -90 ) .

#### Definition of factor pairs?

In mathematics, factor pair are often given as pair of numbers which when multiplied together give the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 90 are 1 , 2 , 3 , 5 , 6 , 9 , 10 , 15 , 18 , 30 , 45 , 90. So, factors of 90 in pair are (1,90), (2,45), (3,30), (5,18), (6,15), (9,10).

#### What are factors?

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

#### Properties of Factors

• Each number is a factor of itself. Eg. 90 is a factor of itself.
• 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, 5, 6, 9, 10, 15, 18, 30, 45, 90 are exact divisors of 90.
• 1 is a factor of every number. Eg. 1 is a factor of 90.
• Every number is a factor of zero (0), since 90 x 0 = 0.

#### Steps to find Factors of 90

• Step 1. Find all the numbers that would divide 90 without leaving any remainder. Starting with the number 1 upto 45 (half of 90). The number 1 and the number itself are always factors of the given number.
90 ÷ 1 : Remainder = 0
90 ÷ 2 : Remainder = 0
90 ÷ 3 : Remainder = 0
90 ÷ 5 : Remainder = 0
90 ÷ 6 : Remainder = 0
90 ÷ 9 : Remainder = 0
90 ÷ 10 : Remainder = 0
90 ÷ 15 : Remainder = 0
90 ÷ 18 : Remainder = 0
90 ÷ 30 : Remainder = 0
90 ÷ 45 : Remainder = 0
90 ÷ 90 : Remainder = 0

Hence, Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

• Is 90 a composite number?

Yes 90 is a composite number.

• Is 90 a prime number?

No 90 is not a prime number.

• What is the mean of factors of 90?

Factors of 90 are 1 , 2 , 3 , 5 , 6 , 9 , 10 , 15 , 18 , 30 , 45 , 90. therefore mean of factors of 90 is (1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90) / 12 = 19.50.

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

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. So, factors of 90 in pair are (1,90), (2,45), (3,30), (5,18), (6,15), (9,10).

Sammy wants to write all the negative factors of 90 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 90 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, -90. Hence, factors of 90 in pair are (-1,-90), (-2,-45), (-3,-30), (-5,-18), (-6,-15), (-9,-10).

Help Deep in writing the positive factors of 90 in pair and negative factor of 90 in pair.

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Positive factors of 90 in pair are (1,90), (2,45), (3,30), (5,18), (6,15), (9,10). Negative factors of 90 in pair are (-1,-90), (-2,-45), (-3,-30), (-5,-18), (-6,-15), (-9,-10).

Find the product of all prime factors of 90.

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. Prime factors are 2, 3, 3, 5. So, the product of all prime factors of 90 would be 2 x 3 x 3 x 5 = 90.

Can you help Sammy list the factors of 90 and also find the factor pairs?

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Factors of 90 in pair are (1,90), (2,45), (3,30), (5,18), (6,15), (9,10).

Help Diji in finding factors of 90 by Prime Factorization method and then sorting factors of 90 in pairs.

Prime factorization of 90 is 2 x 3 x 3 x 5. Factors of 90 in pair can be written as (1,90), (2,45), (3,30), (5,18), (6,15), (9,10).

Write the smallest prime factor of 90.

Smallest prime factor of 90 is 2.

Write the largest prime factor of 90.

Largest prime factor of 90 is 5.