What are the Factors of 49?

The following are the different types of factors of 49:

• Factors of 49: 1, 7, 49

• Sum of Factors of 49: 57

• Negative Factors of 49: -1, -7, -49

• Prime Factors of 49: 7

• Prime Factorization of 49: 7^2

There are two ways to find the factors of 49: using factor pairs, and using prime factorization.

Factor pairs of 49 are any two numbers that, when multiplied together, equal 49. The question to ask is “what two numbers multiplied together equal 49?” Every factor can be paired with another factor, and multiplying the two will result in 49.

To find the factor pairs of 49, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 49. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 7.

Step 2:

Divide 49 by the smallest prime factor, in this case, 7:

49 ÷ 7 = 7

7 and 7 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 7 as the new focus. Find the smallest prime factor that isn’t 1, and divide 7 by that number. In this case, 7 is the new smallest prime factor:

7 ÷ 7 = 1

Remember that this new factor pair is only for the factors of 7, not 49. So, to finish the factor pair for 49, you’d multiply 7 and 7 before pairing with 1:

7 x 7 = 49

Step 4:

Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.

Here are all the factor pairs for 49:

(1, 49), (7, 7)

So, to list all the factors of 49: 1, 7, 49

The negative factors of 49 would be: -1, -7, -49

To find the Prime factorization of 49, we break down all the factors of 49 until we are left with only prime factors. We then express n as a product of multiplying the prime factors together.

The process of finding the prime factorization of 49 only has a few differences from the above method of finding the factors of 49. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.

Here are the steps for finding the prime factorization of 49:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 49. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 7.

Step 2:

Divide 49 by the smallest prime factor, in this case, 7

49 ÷ 7 = 7

7 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 7 as the new focus. Find the smallest prime factor that isn’t 1, and divide 7 by that number. The smallest prime factor you pick for 7 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.

So, the unique prime factors of 49 are: 7

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 14 - The factors of 14 are 1, 2, 7, 14

Factors of 86 - The factors of 86 are 1, 2, 43, 86

Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28

Factors of 16 - The factors of 16 are 1, 2, 4, 8, 16