Factors of 18

What are the factors of 18? The factors of 18 are the numbers that completely divide 18 without leaving a remainder. Thus we can say that the factors of 18 are the divisors of 18. In this section, we will learn about the factors of 18 and the prime factors of 18.

For more details, visit  Basic concepts of factors

Highlights of Factors of 18

  • 18=2×3×3 is the prime factorization of 18.
  • The factors of 18 are 1, 2, 3, 6, 9, and 18.
  • 2 and 3 are the prime factors of 18.
  • The negative factors of 18 are –1, -2, -3, -6, -9, and –18.

What are the factors of 18?

To get the factors of 18, we will first write the number 18 multiplicatively in all possible ways. We have:

18 = 1×18 

18 = 2×9

18 = 3×6

Note that there are no numbers between 3 and 6 that can divide 18. So we will stop writing 18 multiplicatively. Hence the factors of 18 in pairs are given as follows:

18 = a×bFactors in Pairs (a,b)
18 = 1×18 (1, 18)
18 = 2×9(2, 9)
18 = 3×6(3, 6)

Thus the pair factors of 18 are (1, 18), (2, 9), and (3, 6). Note that all the numbers appearing in pair factors are the factors of 18.

∴ we conclude that

The factors of 18 are:

1, 2, 3, 6, 9, and 18.

Number of factors of 18

The factors of 18 are 1, 2, 3, 6, 9, and 18.

Therefore the total number of factors of 18 is six.

Prime Factors of 18

We have found above that the factors of 18 are 1, 2, 3, 6, 9, and 18. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 18 are 2 and 3.

Question: What are the factors of 18?

Video Solution:

How to find factors of 18?

By division method, we will determine the factors of 18. In this method, we will find the numbers that can divide 18 completely with the remainder zero. See that

18/1=18 and the remainder is 0.1 and 18 are factors of 18.
18/2=9 and the remainder is 0.2 and 9 are factors of 18.
18/3=6 and the remainder is 0.3 and 6 are factors of 18.

Note that no numbers other than the numbers in violet color can divide 18. So the numbers in violet color, that is, 1, 2, 3, 6, 9, and 18 are the complete list of factors of 18.

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