Factors of 66

Definition of factors of 66: If a number completely divides 66 without leaving a remainder, then that number is called a factor of 66. Thus, we can say that the factors of 66 are the divisors of 66.

Here, we will learn about the factors of 66 and the prime factors of 66. We have:

  • 66 = 2×3×11 is the prime factorization of 66.
  • The factors of 66 are 1, 2, 3, 6, 11, 22, 33 and 66.
  • The prime factors of 66 are 2, 3 and 11.
  • Negative factors of 66 are –1, -2, -3, -6, -11, -22, -33 and –66.

What are the factors of 66?

Let us write the number 66 multiplicatively in all possible ways. We definitely have:

66 = 1×66 

66 = 2×33

66 = 3×22

66 = 6×11

As there are no other ways we can write 66 multiplicatively, so we will stop right now. So the factors of 66 in pairs are given as follows:

66 = a×b Factors in Pairs (a,b)
66 = 1×66  (1, 66)
66 = 2×33 (2, 33)
66 = 3×22 (3, 22)
66 = 6×11 (6, 11)

Thus the pair factors of 66 are (1, 66), (2, 33), (3, 22) and (6, 11). As all the numbers appearing in pair factors are the factors of 66, we conclude that

The factors of 66 are:

1, 2, 3, 6,11, 22, 33 and 66.

Number of factors of 66

From above we have calculated the factors of 66 which are 1, 2, 3, 6, 11, 22, 33 and 66.

Thus the total number of factors of 66 is eight.

Prime Factors of 66

Note that the factors of 66 are 1, 2, 3, 6, 11, 22, 33 and 66. Among those factors, we observe that only 2, 3 and 11 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 66 are 2, 3 and 11.

Question: What are the factors of 66?

Video Solution:

How to find factors of 66?

Now we will determine the factors of 66 by division method. In this method, we will try to find the numbers that can divide 66 with no remainder. See that

66/1=66 and the remainder is 0.

1 and 66 are factors of 66.

66/2=33 and the remainder is 0.

2 and 33 are factors of 66.

66/3=22 and the remainder is 0.

3 and 22 are factors of 66.

66/6=11 and the remainder is 0.

6 and 11 are factors of 66.

Note that no numbers other than the numbers in violet color can divide 66. So the numbers in violet color, that is, 1, 2, 3, 6, 11, 22, 33, and 66 are the complete list of factors of 66.

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