What are the Factors of 85?

Factors of 85 Methods What are the Factors of 85? The following are the different types of factors of 85: • Factors of 85: 1, 5, 17, 85 • Sum of Factors of 85: 108 • Negative Factors of 85: -1, -5, -17, -85 • Prime Factors of 85: 5, 17 • Prime Factorization of 85: 5^1 × 17^1 There are two ways to find the factors of 85: using factor pairs, and using prime factorization. The Factor Pairs of 85 Factor pairs of 85 are any two numbers that, when multiplied together, equal 85. The question to ask is “what two numbers multiplied together equal 85?” Every factor can be paired with another factor, and multiplying the two will result in 85. To find the factor pairs of 85, follow these steps: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 85. 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 5. Step 2: Divide 85 by the smallest prime factor, in this case, 5: 85 ÷ 5 = 17 5 and 17 will make a new factor pair. Step 3: Repeat Steps 1 and 2, using 17 as the new focus. Find the smallest prime factor that isn’t 1, and divide 17 by that number. In this case, 17 is the new smallest prime factor: 17 ÷ 17 = 1 Remember that this new factor pair is only for the factors of 17, not 85. So, to finish the factor pair for 85, you’d multiply 5 and 17 before pairing with 1: 5 x 17 = 85 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 85: (1, 85), (5, 17) So, to list all the factors of 85: 1, 5, 17, 85 The negative factors of 85 would be: -1, -5, -17, -85 Prime Factorization of 85 To find the Prime factorization of 85, we break down all the factors of 85 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 85 only has a few differences from the above method of finding the factors of 85. 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 85: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 85. 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 5. Step 2: Divide 85 by the smallest prime factor, in this case, 5 85 ÷ 5 = 17 5 becomes the first number in our prime factorization. Step 3: Repeat Steps 1 and 2, using 17 as the new focus. Find the smallest prime factor that isn’t 1, and divide 17 by that number. The smallest prime factor you pick for 17 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 85 are: 5, 17 Find the Factors of Other Numbers Practice your factoring skills by exploring how to factor other numbers, like the ones below: Factors of 134 - The factors of 134 are 1, 2, 67, 134 Factors of 112 - The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42