1. Steps to find factors of 66 using Division Method

Example: Find factors of 66

  • Divide 66 by 1: 66 ÷ 1 : Remainder = 0
  • Divide 66 by 2: 66 ÷ 2 : Remainder = 0
  • Divide 66 by 3: 66 ÷ 3 : Remainder = 0
  • Divide 66 by 6: 66 ÷ 6 : Remainder = 0
  • Divide 66 by 11: 66 ÷ 11 : Remainder = 0
  • Divide 66 by 22: 66 ÷ 22 : Remainder = 0
  • Divide 66 by 33: 66 ÷ 33 : Remainder = 0
  • Divide 66 by 66: 66 ÷ 66 : Remainder = 0

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

2. Steps to find factors of 66 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 66 using the division method, follow these steps:

  • Step 1. Start dividing 66 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 66, which is 2. Divide 66 by 2 to obtain the quotient (33).
    66 ÷ 2 = 33
  • Step 3. Repeat step 1 with the obtained quotient (33).
    33 ÷ 3 = 11
    11 ÷ 11 = 1

So, the prime factorization of 66 is, 66 = 2 x 3 x 11.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 66 as shown below:

So, the prime factorization of 66 is, 66 = 2 x 3 x 11.

3. Find factors of 66 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 66 would be the two numbers which, when multiplied, give 66 as the result.

The following table represents the calculation of factors of 66 in pairs:

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 ) , ( -2 , -33 ) , ( -3 , -22 ) and ( -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.

Frequently Asked Questions

  • What are the prime factors of 66?

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

  • What two numbers make 66?

    Two numbers that make 66 are 2 and 33.

  • What is the greatest prime factors of 66?

    The greatest prime factor of 66 is 11.

  • What are factors of 66?

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

  • How do you find factors of a negative number? ( eg. -66 )?

    Factors of -66 are -1, -2, -3, -6, -11, -22, -33, -66.

  • What are five multiples of 66?

    First five multiples of 66 are 132, 198, 264, 330, 396.

  • Write some multiples of 66?

    First five multiples of 66 are 132, 198, 264, 330.

  • Is 66 a perfect square?

    No 66 is not a perfect square.

  • What two numbers make 66?

    Two numbers that make 66 are 2 and 33.

Examples of Factors

What is prime factorization of 66?

Prime factorization of 66 is 2 x 3 x 11 = 2 x 3 x 11.

Sammy is puzzled while calculating the prime factors of 66. Can you help him find them?

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Prime factors of 66 are 2, 3, 11

Kevin has been asked to write 7 factor(s) of 66. Can you predict the answer?

7 factor(s) of 66 are 1, 2, 3, 6, 11, 22, 33.

Joey wants to write all the prime factors of 66 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 66 are 2, 3, 11.
So in exponential form it can be written as 2 x 3 x 11.

How many factors are there for 66?

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 66? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 11, 22, 33, 66.
Negative factors are -1, -2, -3, -6, -11, -22, -33, -66.

Can you help Rubel to find out the product of the even factors of 66?

Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66.
Even factors of 66 are 2, 6, 22, 66.
Hence, product of even factors of 66 is; 2 x 6 x 22 x 66 = 17424.