What are the Factors of 675?

Factors of 675 Methods What are the Factors of 675? The following are the different types of factors of 675: • Factors of 675: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675 • Sum of Factors of 675: 1240 • Negative Factors of 675: -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225, -675 • Prime Factors of 675: 3, 5 • Prime Factorization of 675: 3^3 × 5^2 There are two ways to find the factors of 675: using factor pairs, and using prime factorization. The Factor Pairs of 675 Factor pairs of 675 are any two numbers that, when multiplied together, equal 675. The question to ask is “what two numbers multiplied together equal 675?” Every factor can be paired with another factor, and multiplying the two will result in 675. To find the factor pairs of 675, follow these steps: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 675. 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 3. Step 2: Divide 675 by the smallest prime factor, in this case, 3: 675 ÷ 3 = 225 3 and 225 will make a new factor pair. Step 3: Repeat Steps 1 and 2, using 225 as the new focus. Find the smallest prime factor that isn’t 1, and divide 225 by that number. In this case, 3 is the new smallest prime factor: 225 ÷ 3 = 75 Remember that this new factor pair is only for the factors of 225, not 675. So, to finish the factor pair for 675, you’d multiply 3 and 3 before pairing with 75: 3 x 3 = 9 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 675: (1, 675), (3, 225), (5, 135), (9, 75), (15, 45), (25, 27) So, to list all the factors of 675: 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675 The negative factors of 675 would be: -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225, -675 Prime Factorization of 675 To find the Prime factorization of 675, we break down all the factors of 675 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 675 only has a few differences from the above method of finding the factors of 675. 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 675: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 675. 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 3. Step 2: Divide 675 by the smallest prime factor, in this case, 3 675 ÷ 3 = 225 3 becomes the first number in our prime factorization. Step 3: Repeat Steps 1 and 2, using 225 as the new focus. Find the smallest prime factor that isn’t 1, and divide 225 by that number. The smallest prime factor you pick for 225 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 675 are: 3, 5 Find the Factors of Other Numbers Practice your factoring skills by exploring how to factor other numbers, like the ones below: Factors of 21 - The factors of 21 are 1, 3, 7, 21 Factors of 29 - The factors of 29 are 1, 29 Factors of 8 - The factors of 8 are 1, 2, 4, 8 Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42