Factors of 33

Definition of factors of 33: If a number completely divides 33 with the remainder zero, then that number is called a factor of 33.

By the above definition, we can say that the factors of 33 are the divisors of 33. In this section, we will learn about the factors of 33 and the prime factors of 33.

Also Read: Basic concepts of factors

Highlights of Factors of 33

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

What are the factors of 33?

We first write the number 33 multiplicatively in all possible ways. Note that we have:

33 = 1×33 

33 = 3×11

As we cannot express 33 multiplicatively in any other way, so we will stop right now. Thus the factors of 33 in pairs are given as follows:

33 = a×b Factors in Pairs (a,b)
33 = 1×33  (1, 33)
33 = 3×11 (3, 11)

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

The factors of 33 are:

1, 3, 11 and 33.

Number of factors of 33

From above we have calculated the factors of 33 which are 1, 3, 11 and 33. Thus the total number of factors of 33 is four.

Prime Factors of 33

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

∴ the prime factor of 33 are 3 and 11.

Question: What are the factors of 33?

Video Solution: 

How to find factors of 33?

Now we will determine the factors of 33 by division method. In this method, we will find the numbers that can divide 33 with no remainder. See that

33/1=33 and the remainder is 0.

1 and 33 are factors of 33.

33/3=11 and the remainder is 0.

3 and 11 are factors of 33.

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