Factors of 70

Definition of factors of 70: If a number completely divides 70 without leaving a remainder, then that number is called a factor of 70. Thus, we can say that the factors of 70 are the divisors of 70.

Here, we will learn about the factors of 70 and the prime factors of 70. We have:

  • 70 = 2×5×7 is the prime factorization of 70.
  • The factors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70.
  • The prime factors of 70 are 2, 5 and 7.
  • Negative factors of 70 are –1, -2, -5, -7, -10, -14, -35 and –70.

What are the factors of 70?

Let us write the number 70 multiplicatively in all possible ways. We definitely have:

70 = 1×70 

70 = 2×35

70 = 5×14

70 = 7×10

As there are no other ways we can write 70 multiplicatively, so we will stop right now. So the factors of 70 in pairs are given as follows:

70 = a×b Factors in Pairs (a,b)
70 = 1×70  (1, 70)
70 = 2×35 (2, 35)
70 = 5×14 (5, 14)
70 = 7×10 (7, 10)

Thus the pair factors of 70 are (1, 70), (2, 35), (5, 14), and (7, 10). As all the numbers appearing in pair factors are the factors of 70, we conclude that

The factors of 70 are:

1, 2, 5, 7, 10, 14, 35 and 70.

Number of factors of 70

From above we have calculated the factors of 70 which are 1, 2, 5, 7, 10, 14, 35, and 70.

Thus the total number of factors of 70 is eight.

Prime Factors of 70

Note that the factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. Among those factors, we observe that only 2, 5 and 7 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 70 are 2, 5 and 7.

Question: What are the factors of 70?

Video Solution:

How to find factors of 70?

Now we will determine the factors of 70 by division method. In this method, we will try to find the numbers that can divide 70 with no remainder. See that

70/1=70 and the remainder is 0.

1 and 70 are factors of 70.

70/2=35 and the remainder is 0.

2 and 35 are factors of 70.

70/5=14 and the remainder is 0.

5 and 14 are factors of 70.

70/7=10 and the remainder is 0.

7 and 10 are factors of 70.

Note that no numbers other than the numbers in violet color can divide 70. So the numbers in violet color, that is, 1, 2, 5, 7, 10, 14, 35, and 70 are the complete list of factors of 70.

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