Factors of 66

The factors of 66 are the numbers that divide 66 evenly without leaving a remainder. In other words, the numbers which are multiplied in pairs resulting in the original number 66 are the factors of 66. For example, the pair factor of 66 is represented by (1, 66) or (-1, -66). If we multiply -1 and -66, it will result in the original number. Hence, the factors and the pair factors of 66 can be positive or negative, but they cannot be in decimal or fraction form. In this article, we will learn the factors of 66, pair factors, and the prime factors of 66 using the prime factorization method and many solved examples.

Table of Contents:

What are the Factors of 66?

The numbers that divide 66 evenly and leave a remainder 0 are called the factors of 66. As 66 is an even composite number, it has many factors other than 1 and 66. Hence, the factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. Similarly, the negative factors of 66 are -1, -2, -3, -6, -11, -22, -33, and -66.

Factors of 66: 1, 2, 3, 6, 11, 22, 33, and 66.

Prime Factorization of 66: 2 × 3 × 11

Pair Factors of 66

The pair of numbers which are multiplied together, resulting in 66, are the pair factors of 66. The pair factors of 66 can also be expressed in positive and negative form. The positive and negative pair factors of 66 are given below:

Positive Pair Factors of 66:

Positive Factors of 66

Positive Pair Factors of 66

1 × 66

(1, 66)

2 × 33

(2, 33)

3 × 22

(3, 22)

6 × 11

(6, 11)

Hence, the positive pair factors of 66 are (1, 66), (2, 33), (3, 22) and (6, 11).

Negative Pair Factors of 66:

Negative Factors of 66

Negative Pair Factors of 66

-1 × -66

(-1, -66)

-2 × -33

(-2, -33)

-3 × -22

(-3, -22)

-6 × -11

(-6, -11)

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

Factors of 66 by Division Method

The factors of 66 are found using the division method. In this method, the number 66 is divided by different integers. If the integers divide 66 evenly without leaving a remainder, then those integers are the factors of 66. Now, let’s start dividing 66 by 1 and continue with the different integers.

  • 66/1 = 66 (Factor is 1 and Remainder is 0)
  • 66/2 = 33 (Factor is 2 and Remainder is 0)
  • 66/3 = 22 (Factor is 3 and Remainder is 0)
  • 66/6 = 11 (Factor is 6 and Remainder is 0)
  • 66/11 = 6 (Factor is 11 and Remainder is 0)
  • 66/22 = 3 (Factor is 22 and Remainder is 0)
  • 66/33 = 2 (Factor is 33 and Remainder is 0)
  • 66/66 = 1 (Factor is 66 and Remainder is 0)

If any numbers other than 1, 2, 3, 6, 11, 22, 33 and 66 divide 66, it leaves a remainder of some value. Hence, the factors of 66 are 1, 2, 3, 6, 11, 22, 33 and 66.

Prime Factorization of 66

In the prime factorization of 66, the number 66 is written as the product of its prime factors. The prime factors of 66 are found as follows:

Take the pair factor of 66, say (1, 66)

Here, factor 1 is neither prime nor composite, and it cannot be split further. So, take the other factor, 66, which is an even composite number.

Now, split the number 66 into its prime factors, say 6 × 11. Now, 11 is a prime number, and 6 is a composite number, which is further factored into 2 × 3.

Hence, the number 66 is written as 2 × 3 × 11, and the prime factors of 66 are 2, 3 and 11.

Therefore, the prime factorization of 66 is 2 × 3 × 11.

Solved Examples

Example 1:

What are the common factors of 66 and 33?

Solution:

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

The factors of 33 are 1, 3, 11 and 33.

Hence, the common factors of 66 and 33 are 1, 3, 11 and 33.

Example 2:

Find the common factors of 66 and 65.

Solution:

Factors of 66 = 1, 2, 3, 6, 11, 22, 33, and 66.

Factors of 65 = 1, 5, 13 and 65.

Thus, the common factor of 66 and 65 is 1.

Example 3:

Find the common factors of 66 and 67.

Solution:

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

The factors of 67 are 1 and 67.

As 67 is a prime number, the common factor of 66 and 67 is 1.


Frequently Asked Questions on Factors of 66

What are the factors of 66?

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

What is the prime factorization of 66?

The prime factorization of 66 is 2 × 3 × 11.

What are the positive pair factors of 66?

The positive pair factors of 66 are (1, 66), (2, 33), (3, 22) and (6, 11).

What are the negative pair factors of 66?

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

Is 33 a factor of 66?

Yes, 33 is a factor of 66. As 33 divides 66 exactly and leaves a remainder 0, the number 33 is a factor of 66.

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