What are the Factors of 142?

The following are the different types of factors of 142:

• Factors of 142: 1, 2, 71, 142

• Sum of Factors of 142: 216

• Negative Factors of 142: -1, -2, -71, -142

• Prime Factors of 142: 2, 71

• Prime Factorization of 142: 2^1 × 71^1

There are two ways to find the factors of 142: using factor pairs, and using prime factorization.

Factor pairs of 142 are any two numbers that, when multiplied together, equal 142. The question to ask is “what two numbers multiplied together equal 142?” Every factor can be paired with another factor, and multiplying the two will result in 142.

To find the factor pairs of 142, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 142. 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 2.

Step 2:

Divide 142 by the smallest prime factor, in this case, 2:

142 ÷ 2 = 71

2 and 71 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 71 as the new focus. Find the smallest prime factor that isn’t 1, and divide 71 by that number. In this case, 71 is the new smallest prime factor:

71 ÷ 71 = 1

Remember that this new factor pair is only for the factors of 71, not 142. So, to finish the factor pair for 142, you’d multiply 2 and 71 before pairing with 1:

2 x 71 = 142

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 142:

(1, 142), (2, 71)

So, to list all the factors of 142: 1, 2, 71, 142

The negative factors of 142 would be: -1, -2, -71, -142

To find the Prime factorization of 142, we break down all the factors of 142 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 142 only has a few differences from the above method of finding the factors of 142. 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 142:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 142. 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 2.

Step 2:

Divide 142 by the smallest prime factor, in this case, 2

142 ÷ 2 = 71

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 71 as the new focus. Find the smallest prime factor that isn’t 1, and divide 71 by that number. The smallest prime factor you pick for 71 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 142 are: 2, 71

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

Factors of 29 - The factors of 29 are 1, 29

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

Factors of 18 - The factors of 18 are 1, 2, 3, 6, 9, 18

Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63