Factors of 150

Definition of factors of 150: If a number completely divides 150 without leaving a remainder, then that number is called a factor of 150.  Here, we will learn about the factors of 150 and the prime factors of 150. We have:

  • 150 = 2×3×5×5 = 2 × 3 × 52 is the prime factorization of 150
  • The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150
  • The prime factors of 150 are 2, 3 and 5.
  • Negative factors of 150 are -1, -2, -3, -5, -6, -10, -15, -25, -30, -50, -75 and -150.

What are the factors of 150?

Let us write the number 150 multiplicatively in all possible ways. We definitely have:

150 = 1×150 

150 = 2×75

150 = 3×50

150 = 5×25

150 = 6×25

150 = 10×15

As there are no other ways we can write 150 multiplicatively, so we will stop right now. So the factors of 150 in pairs are given as follows:

150 = a×b Factors in Pairs (a,b)
150 = 1×150  (1, 150)
150 = 2×75 (2, 75)
150 = 3×50 (3, 50)
150 = 5×30
(5, 30)
150 = 6×25 (6, 25)
150 = 10×15 (10, 15)

Thus the pair factors of 150 are (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), and (10, 15). As all the numbers appearing in pair factors are the factors of 150, we conclude that

The factors of 150 are:

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

Number of factors of 150

From above we have calculated the factors of 150 which are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

Thus the total number of factors of 150 is twelve.

Prime Factors of 150

Note that the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. Among these factors, we observe that only 2, 3 and 5 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 150 are 2, 3 and 5.

Question: What are the factors of 150?

Video Solution:

How to find factors of 150?

Now we will determine the factors of 150 by division method. In this method, we will try to find the numbers that can divide 150 with the remainder zero. See that

150/1=150 and the remainder is 0. 1 and 150 are factors of 150.
150/2=75 and the remainder is 0. 2 and 75 are factors of 150.
150/3=50 and the remainder is 0. 3 and 50 are factors of 150.
150/5=30 and the remainder is 0. 5 and 30 are factors of 150.
150/6=25 and the remainder is 0. 6 and 25 are factors of 150.
150/10=15 and the remainder is 0. 10 and 15 are factors of 150.

Note that no numbers other than the numbers in violet color can divide 150. So the numbers in violet color, that is, 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150 are the complete list of factors of 150.

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