Factors of 66 | Prime Factorization of 66 | Factor Tree of 66

The numbers that can divide the given number 66 thoroughly and evenly are known as factors of 66. In this article, you will learn about the factors of 66 using the prime factorization method, long division method, and factor tree method.

What Are the Factors of 66?

The numbers that divide the given number 66 thoroughly without leaving behind any remainder are known as the factors of 66. There are positive and negative factors for a number. The factors of a number can be categorized as prime numbers and composite numbers. Prime numbers have two or less than two numbers as the factors as opposed to composite numbers that have more than two numbers as their factors. Here, the number 66 is a composite number as it has more than two numbers as its factors. The 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.

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

Prime Factorization of 66: 2 x 3 x 11

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

Prime Factors of 66: 2, 3, and 11.

Sum of Factors of 66: 144

Sum of Prime Factors of 66: 16

What Are the Factors of 66 in Pairs?

There exist both positive and negative pair factors for a number. The pair factor of the given number 66 is defined as a combination of two numbers which on multiplying with each other gives 66 as the result.

Positive Pair Factors of 66

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

Negative Pair Factors of 66

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

What Is the Prime Factorization of 66?

Prime factorization is a method used to identify the prime factors of a given number. The following are the steps involved in the prime factorization of 66.

• Step 1: Let’s place the number 66 at the top, and divide it by the smallest number that can divide the given number 66 without any decimals and it is 2.
  66 ÷ 2 = 33
• Step 2: We get 33, as the quotient, and again it’s divisible by the number 3.
  33 ÷ 3 = 11
• Step 3: And now the numbers 3 and 11 are prime numbers, we can’t further divide them as they are divisible by themselves.
• Step 4: So, now let’s circle the numbers 3 and 11.

Therefore, the prime factors of 66 are 2, 3, and 11. Below is an image representation of the factor tree of 66.

How to Find Factors of 66 Through Division Method?

The long-division method can be used to find out the factors of 66. In this method, the number 66 is divided by a sequence of numbers that can divide the given number 66 without any decimal points in the quotient. And those numbers are the factors of 66. The following are the steps through which we can identify the factors of 66.

• 66 ÷ 1 = 66
• 66 ÷ 2 = 33
• 66 ÷ 3 = 22
• 66 ÷ 11 = 6
• 66 ÷ 22 = 3
• 66 ÷ 33 = 2
• 66 ÷ 66 = 1

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

What Is the Factor Tree of 66?

A factor tree is another method through which we can find out the prime factors of the given number 66. In this method, let’s place the number 66 at the top of the factor tree. Now, split the pair factors of the number into two branches and this process should be continued until the numbers in the branches cannot be divided further. And then circle those numbers, as they are the prime factors of 66.

• Step 1: Let’s place the number 66 at the top of the factor tree and write down the pair factors 2, and 33 in two branches.
  66 ÷ 2 = 33
• Step 2: Now let’s put the pair factors of 33 in the branches, which are 3 and 11.
  33 ÷ 3 = 11
• Step 3: And now the numbers 3 and 11 are prime numbers, we can’t further divide them as they are divisible by themselves.
• Step 4: And in the final step, we get 1 as the quotient and it cannot be divided further. So the prime factors of 99 are 3, and 11.

Therefore, the prime factors of 66 are 2, 3, and 11. Below is a visual representation of the factor tree of 66.

Solved Examples of 66 Are:

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

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

What is the sum of prime factors of 66?
The sum of the prime factors of 66 is 16.

What are the negative factors of 66?
The negative factors of 66 are -1, -2, -3, -6, -11, -22, -33, and -66.

Frequently Asked Questions

What are the factors pairs of 66?
The pair factors of 66 are (1, 66), (2, 33), (3, 22), and (6, 11).

How many divisors does 66 have?
The list of divisors is 1,2,3,6,11,22,33,66.

What are the multiples of 66?
The first 10 multiples of 66 are 66, 132, 198, 264, 330, 396, 462, 528, 594, and 660.

What is the prime factor of 66?
The prime factors of 66 are 2, 3, and 11.

Is 66 a prime or composite?
66 is a composite number, as it has more than two factors.