Factors of 49

Definition of factors of 49: If a number completely divides 49 without leaving a remainder, then that number is called a factor of 49.

By the above definition, we can say that the factors of 49 are the divisors of 49. In this section, we will learn about the factors of 49 and the prime factors of 49.

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Highlights of Factors of 49

  • 49=7×7 is the prime factorization of 49.
  • The factors of 49 are 1, 7 and 49.
  • The only prime factor of 49 is 7.
  • The negative factors of 49 are –1, -7 and –49.

What are the factors of 49?

First, we write the number 49 multiplicatively in all possible ways. We have:

49 = 1×49 

49 = 7×7

We cannot write 49 multiplicatively in any other way than the above ones, so we will stop right now. Thus the factors of 49 in pairs are given as follows:

49 = a×b Factors in Pairs (a,b)
49 = 1×49  (1, 49)
49 = 7×7 (7, 7)

Thus the pair factors of 49 are (1, 49) and (7, 7). As all the numbers appearing in pair factors are the factors of 49, we conclude that

The factors of 49 are:

1, 7 and 49.

Number of factors of 49

From above we have calculated the factors of 49 which are 1, 7 and 49. Thus the total number of factors of 49 is three.

Prime Factors of 49

Note that the factors of 49 are 1, 7 and 49. Among those factors, we observe that only 7 is a prime number as 7 does not have any proper divisors.

∴ the only prime factor of 49 is 7.

Question: What are the factors of 49?

Video Solution:

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How to find factors of 49?

Now we will determine the factors of 49 by division method. In this method, we will try to find the numbers that can divide 49 with no remainder. See that

49/1=49 and the remainder is 0.

1 and 49 are factors of 49.

49/7=7 and the remainder is 0.

7 and 7 are factors of 49 ⇒ 7 is a factor of 49.

Note that no numbers other than the numbers in violet color can divide 49. So the numbers in violet color, that is, 1, 7 and 49 are the complete list of factors of 49.