Factors of 66 | Prime factors of 66
Factors of 66 | Prime factors of 66

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Factors of 66

Factors of 66 are the numbers which when multiplied in pairs give the product as 66. These factors can be negative as well. The number 66 is an even composite number. In this lesson, we will learn how to calculate the factors of 66, the prime factors of 66, and the factors of 66 in pairs along with solved examples for a better understanding.

  • Factors of 66: 1, 2, 3, 6, 11, 22, 33, and 66
  • Prime Factorization of 66: 66 = 2 × 3 × 11
1. What Are the Factors of 66?
2. How to Calculate the Factors of 66?
3. Important Notes
4. Factors of 66 by Prime Factorization
5. Factors of 66 in Pairs
6. FAQs on Factors of 66
7. Challenging Questions

What Are the Factors of 66?

Let us first understand about factors.

The number 66 is a composite number. To understand why it is composite, let’s recall the definition of a composite number.

A composite number is a number that consists of more than two factors.

For instance, consider 70. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. Therefore, 70 is a composite number.

We will look at another example.

Consider the number 43. The factors of 43 are 1 and 43.

Since it has only two factors, it is a prime number.

Coming back to the number 66.

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

How did we get this?

Let us discuss this in the next section.

First, divide 66 with the smallest whole number, i.e., 1.

Is the remainder zero? Yes! So, we will get

66 ÷ 1 = 66

66 × 1 = 66

Now we will follow the same procedure with the number 2.

Is the remainder zero? Yes!

66 ÷ 2 = 33

33 × 2 = 66

If a number is divisible by another number, leaving 0 as the remainder, then the number is said to be a factor.

Proceeding in a similar manner, we get the factors of 66.

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

Important Notes:

  • Factors cannot be in decimal form.
  • Factors consist of both positive and negative integers.
  • The number 66 is an even composite number.
  • The number 66 is neither a perfect square number nor a perfect cube number.

Explore factors using illustrations and interactive examples

  • Factors of 70 – The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
  • Factors of 72 – The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
  • Factors of 96 – The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
  • Factors of 60 – The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
  • Factors of 75 – The factors of 75 are 1, 3, 5, 15, 25, and 75.
  • Factors of 68 – The factors of 68 are 1, 2, 4, 17, 34, and 68.

Prime factorization is the process of breaking down a composite number into its prime factors.

To get the prime factorization of 66, we divide it by its smallest prime factor, i.e., 2.

66 ÷ 2 = 33

Now 33 is divided by its smallest prime number, i.e., 3.

33 ÷ 3 = 11

This process goes on till we get the quotient as 1.

The prime factorization of 66 is shown below:

66 = 2 × 3 × 11

It can be presented in a factor tree.

Prime factorization can thus be written as follows 66 = 2 × 3 × 11.

Factors of 66 in Pairs

The two numbers which, when multiplied, give 66 are called the pair factors of 66.

The following are the factors of 66 in pairs.

Challenging Questions:

  • Is -33 a factor of 66?

Factors of 66 Solved Examples

  1. Example 1: Hanna is celebrating her birthday with her classmates. She has 66 chocolates in total and distributes 2 chocolates to each. How many children are there in her class?

    Solution:

    There are 66 chocolates in total.

    She distributes 2 chocolates to each.

    66 ÷ 2 = 33

    Hence, there are 33 children in her class.

  2. Example 2: Rony wants to find the number which is three more than the greatest factor of 66, other than 66. Can you find that number?

    Solution:

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

    Out of these factors, the greatest factor of 66. The next highest factor other than 66 is 33.

    A number which is three more than 33 is 33 + 3 = 36.

    Hence, 36 is the required number

  3. Example 3: Tim has 66 color pens and 22 color pencils. He would like to sell these color pens and pencils together. How many sets of equal color pens and pencils can he make?

    Solution:

    There are 66 color pens and 22 color pencils.

    Therefore, 1 color pencil with 3 color pens makes a set. This means that Tim can make 22 equal sets of colored pens and pencils.

    Thus, Tim will make 22 sets.

Interactive Questions

FAQs 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 are the prime factors of 66?

The prime factors of 66 are 2, 3, and 11.

What is the highest factor of 66?

The highest factor of 66 is 66.

What are the common factors of 66 and 36?

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

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Hence, the common factors are 1, 2, 3, and 6.

What are the common factors of 66 and 44?

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

The factors of 44 are 1, 2, 4, 11, 22, and 44.

Hence, the common factors are 1, 2, 11, and 22.

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