What are the Factors of 138?

Factors of 138 Methods What are the Factors of 138? The following are the different types of factors of 138: • Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138 • Sum of Factors of 138: 288 • Negative Factors of 138: -1, -2, -3, -6, -23, -46, -69, -138 • Prime Factors of 138: 2, 3, 23 • Prime Factorization of 138: 2^1 × 3^1 × 23^1 There are two ways to find the factors of 138: using factor pairs, and using prime factorization. The Factor Pairs of 138 Factor pairs of 138 are any two numbers that, when multiplied together, equal 138. The question to ask is “what two numbers multiplied together equal 138?” Every factor can be paired with another factor, and multiplying the two will result in 138. To find the factor pairs of 138, follow these steps: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 138. 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 138 by the smallest prime factor, in this case, 2: 138 ÷ 2 = 69 2 and 69 will make a new factor pair. Step 3: Repeat Steps 1 and 2, using 69 as the new focus. Find the smallest prime factor that isn’t 1, and divide 69 by that number. In this case, 3 is the new smallest prime factor: 69 ÷ 3 = 23 Remember that this new factor pair is only for the factors of 69, not 138. So, to finish the factor pair for 138, you’d multiply 2 and 3 before pairing with 23: 2 x 3 = 6 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 138: (1, 138), (2, 69), (3, 46), (6, 23) So, to list all the factors of 138: 1, 2, 3, 6, 23, 46, 69, 138 The negative factors of 138 would be: -1, -2, -3, -6, -23, -46, -69, -138 Prime Factorization of 138 To find the Prime factorization of 138, we break down all the factors of 138 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 138 only has a few differences from the above method of finding the factors of 138. 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 138: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 138. 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 138 by the smallest prime factor, in this case, 2 138 ÷ 2 = 69 2 becomes the first number in our prime factorization. Step 3: Repeat Steps 1 and 2, using 69 as the new focus. Find the smallest prime factor that isn’t 1, and divide 69 by that number. The smallest prime factor you pick for 69 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 138 are: 2, 3, 23 Find the Factors of Other Numbers Practice your factoring skills by exploring how to factor other numbers, like the ones below: Factors of 95 - The factors of 95 are 1, 5, 19, 95 Factors of 86 - The factors of 86 are 1, 2, 43, 86 Factors of 44 - The factors of 44 are 1, 2, 4, 11, 22, 44 Factors of 141 - The factors of 141 are 1, 3, 47, 141