Factors of 30

Definition of factors of 30: If a number completely divides 30 with the remainder zero, then that number is called a factor of 30.

By the above definition, we can say that the factors of 30 are the divisors of 30. In this section, we will learn about the factors of 30 and the prime factors of 30.

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Highlights of Factors of 30

  • 30=2×3×5 is the prime factorization of 30.
  • The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.
  • Prime factors of 30 are 2, 3 and 5.
  • Negative factors of 30 are –1, -2, -3, -5, -6, -10, -15 and –30.

What are the factors of 30?

Let us write the number 30 multiplicatively in all possible ways. We have:

30 = 1×30 

30 = 2×15

30 = 3×10

30 = 5×6

As we cannot express 30 multiplicatively in any other way, so we will stop right now. So the factors of 30 in pairs are given as follows:

30 = a×b Factors in Pairs (a,b)
30 = 1×30  (1, 30)
30 = 2×15 (2, 15)
30 = 3×10 (3, 10)
30 = 5×6 (5, 6)

Thus the pair factors of 30 are (1, 30), (2, 15), (3, 10) and (5, 6). As all the numbers appearing in pair factors are the factors of 30, we conclude that

The factors of 30 are:

1, 2, 3, 5, 6, 10, 15 and 30.

Number of factors of 30

From above we have calculated the factors of 30 which are 1, 2, 3, 5, 6, 10, 15 and 30. Thus the total number of factors of 30 is eight.

Prime Factors of 30

Note that the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. Among those factors, we notice that only 2, 3 and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factor of 30 are 2, 3 and 5.

Question: What are the factors of 30?

Video Solution: 

How to find factors of 30?

Now we will determine the factors of 30 by division method. In this method, we will find the numbers that can divide 30 with no remainder. See that

30/1=30 and the remainder is 0.

1 and 30 are factors of 30.

30/2=15 and the remainder is 0.

2 and 15 are factors of 30.

30/3=10 and the remainder is 0.

3 and 10 are factors of 30.

30/5=6 and the remainder is 0.

5 and 6 are factors of 30.

Note that no numbers other than the numbers in violet color can divide 30. So the numbers in violet color, that is, 1, 2, 3, 5, 6, 10, 15 and 30 are the complete list of factors of 30.