# Factors of 66

The factors of 66 are the numbers that divide evenly into 66. There are only four factors of 66: 1, 2, 3, 6, 11, 22, 33, and 66 itself. The prime factorization of 66 is 2 × 3 × 11, which means that 66 is a composite number. Composite numbers are numbers that have more than two factors. The factors of 66 can be used to find the multiples of 66, which are the numbers that can be created by multiplying 66 by one of its factors.

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Prime Numbers

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Some examples of prime numbers include 2, 3, 5, 7, and 11. Prime numbers are important in mathematics as they are used in many mathematical formulas and algorithms, and are also used in the study of number theory.

Composite Numbers

A composite number is a whole number greater than 1 that can be divided evenly by a number other than 1 or itself. In other words, a composite number is not a prime number. Some examples of composite numbers include 4, 6, 8, 9, and 10.

## What are the factors of 66?

The method of calculating the factors of 66 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 66 are the factors of 66.
By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 66 ÷ 1 = 66

This division gives the remainder 0 and so is divisible by 66. So please put them 1 and 66 in your factor list.

1, …. 66

(ii) 66 ÷ 2 = 33

This division gives the remainder 0 and so is divisible by 33. So please put them 2 and 32 in your factor list.

1, 2 …. 33, 66

(iii) 66 ÷ 3 = 22

This division gives the remainder 0 and so is divisible by 22. So please put them 3 and 22 in your factor list.

1, 2, 3 …. 22, 33, 66

(iv) 66 ÷ 6 = 11

This division gives the remainder 0 and so is divisible by 11. So please put them 6 and 11 in your factor list.

1, 2, 3, 6 …. 11, 22, 33, 66

(v) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 2, 3, 6, 11, 22, 33, and 66 are factors of 66.

## Prime Factorization of 66

Prime factorization is the process of writing a number as a product of prime numbers. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

To find the prime factorization of 66, we can use the following steps:

Start by dividing 66 by the smallest prime number, which is 2. 66 ÷ 2 = 33.
33 is not divisible by 2, so we try the next prime number, which is 3. 33 ÷ 3 = 11.
11 is a prime number, so the prime factorization of 66 is 2 × 3 × 11.

Therefore, 2 × 3 × 11 are Prime factorization of 66.

## Factor pairs of 66

Factor pairs of a number are sets of two numbers that, when multiplied together, result in that number.

Let’s determine the factor pairs of 66:

1 and 66
1 × 66 = 66

2 and 33
2 x 33 = 66

3 and 22
3 x 22 = 66

6 and 11
6 x 11 = 66

So, (1, 66), (2, 33), (3, 22) and (6, 11) are factor pairs of 66

## Factor pairs of -66

Let’s determine the factor pairs of 66:

-1 and -66
-1 × -66 = 66

-2 and -33
-2 x -33 = 66

-3 and -22
-3 x -22 = 66

-6 and -11
-6 x -11 = 66

So, (-1, -66), (-2, -33), (-3, -22) and (-6, -11) are negative pair factors of 66

## Factor tree of 66

``````   66
/   \
2    33
/    \
3      11``````

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