# Factors of 66 in pair

Factors of 66 in pair are (1, 66) , (2, 33) , (3, 22) and (6, 11)

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

 1.   Steps to find factors of 66 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 66 in pair

Factor Pair Pair Factorization
1 and 66 1 x 66 = 66
2 and 33 2 x 33 = 66
3 and 22 3 x 22 = 66
6 and 11 6 x 11 = 66

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 66. They are called negative pair factors.

Hence, the negative pairs of 66 would be ( -1 , -66 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 66 are 1 , 2 , 3 , 6 , 11 , 22 , 33 , 66. So, factors of 66 in pair are (1,66), (2,33), (3,22), (6,11).

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 66 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, 6, 11, 22, 33, 66 are exact divisors of 66.
• 1 is a factor of every number. Eg. 1 is a factor of 66.
• Every number is a factor of zero (0), since 66 x 0 = 0.

#### Steps to find Factors of 66

• Step 1. Find all the numbers that would divide 66 without leaving any remainder. Starting with the number 1 upto 33 (half of 66). The number 1 and the number itself are always factors of the given number.
66 ÷ 1 : Remainder = 0
66 ÷ 2 : Remainder = 0
66 ÷ 3 : Remainder = 0
66 ÷ 6 : Remainder = 0
66 ÷ 11 : Remainder = 0
66 ÷ 22 : Remainder = 0
66 ÷ 33 : Remainder = 0
66 ÷ 66 : Remainder = 0

Hence, Factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66

• Is 66 a composite number?

Yes 66 is a composite number.

• Is 66 a prime number?

No 66 is not a prime number.

• What is the mean of factors of 66?

Factors of 66 are 1 , 2 , 3 , 6 , 11 , 22 , 33 , 66. therefore mean of factors of 66 is (1 + 2 + 3 + 6 + 11 + 22 + 33 + 66) / 8 = 18.00.

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

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. So, factors of 66 in pair are (1,66), (2,33), (3,22), (6,11).

Sammy wants to write all the negative factors of 66 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 66 are -1, -2, -3, -6, -11, -22, -33, -66. Hence, factors of 66 in pair are (-1,-66), (-2,-33), (-3,-22), (-6,-11).

Help Deep in writing the positive factors of 66 in pair and negative factor of 66 in pair.

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. Positive factors of 66 in pair are (1,66), (2,33), (3,22), (6,11). Negative factors of 66 in pair are (-1,-66), (-2,-33), (-3,-22), (-6,-11).

Find the product of all prime factors of 66.

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. Prime factors are 2, 3, 11. So, the product of all prime factors of 66 would be 2 x 3 x 11 = 66.

Can you help Sammy list the factors of 66 and also find the factor pairs?

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Factors of 66 in pair are (1,66), (2,33), (3,22), (6,11).

Help Diji in finding factors of 66 by Prime Factorization method and then sorting factors of 66 in pairs.

Prime factorization of 66 is 2 x 3 x 11. Factors of 66 in pair can be written as (1,66), (2,33), (3,22), (6,11).

Write the smallest prime factor of 66.

Smallest prime factor of 66 is 2.

Write the largest prime factor of 66.

Largest prime factor of 66 is 11.