What are the Factors of 148?

The following are the different types of factors of 148:

• Factors of 148: 1, 2, 4, 37, 74, 148

• Sum of Factors of 148: 266

• Negative Factors of 148: -1, -2, -4, -37, -74, -148

• Prime Factors of 148: 2, 37

• Prime Factorization of 148: 2^2 × 37^1

There are two ways to find the factors of 148: using factor pairs, and using prime factorization.

Factor pairs of 148 are any two numbers that, when multiplied together, equal 148. The question to ask is “what two numbers multiplied together equal 148?” Every factor can be paired with another factor, and multiplying the two will result in 148.

To find the factor pairs of 148, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 148. 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 148 by the smallest prime factor, in this case, 2:

148 ÷ 2 = 74

2 and 74 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 74 as the new focus. Find the smallest prime factor that isn’t 1, and divide 74 by that number. In this case, 2 is the new smallest prime factor:

74 ÷ 2 = 37

Remember that this new factor pair is only for the factors of 74, not 148. So, to finish the factor pair for 148, you’d multiply 2 and 2 before pairing with 37:

2 x 2 = 4

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 148:

(1, 148), (2, 74), (4, 37)

So, to list all the factors of 148: 1, 2, 4, 37, 74, 148

The negative factors of 148 would be: -1, -2, -4, -37, -74, -148

To find the Prime factorization of 148, we break down all the factors of 148 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 148 only has a few differences from the above method of finding the factors of 148. 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 148:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 148. 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 148 by the smallest prime factor, in this case, 2

148 ÷ 2 = 74

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 74 as the new focus. Find the smallest prime factor that isn’t 1, and divide 74 by that number. The smallest prime factor you pick for 74 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 148 are: 2, 37

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

Factors of 17 - The factors of 17 are 1, 17

Factors of 12 - The factors of 12 are 1, 2, 3, 4, 6, 12

Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98

Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144