What are the Factors of 468?

Factors of 468 Methods What are the Factors of 468? The following are the different types of factors of 468: • Factors of 468: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 • Sum of Factors of 468: 1274 • Negative Factors of 468: -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, -468 • Prime Factors of 468: 2, 3, 13 • Prime Factorization of 468: 2^2 × 3^2 × 13^1 There are two ways to find the factors of 468: using factor pairs, and using prime factorization. The Factor Pairs of 468 Factor pairs of 468 are any two numbers that, when multiplied together, equal 468. The question to ask is “what two numbers multiplied together equal 468?” Every factor can be paired with another factor, and multiplying the two will result in 468. To find the factor pairs of 468, follow these steps: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 468. 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 468 by the smallest prime factor, in this case, 2: 468 ÷ 2 = 234 2 and 234 will make a new factor pair. Step 3: Repeat Steps 1 and 2, using 234 as the new focus. Find the smallest prime factor that isn’t 1, and divide 234 by that number. In this case, 2 is the new smallest prime factor: 234 ÷ 2 = 117 Remember that this new factor pair is only for the factors of 234, not 468. So, to finish the factor pair for 468, you’d multiply 2 and 2 before pairing with 117: 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 468: (1, 468), (2, 234), (3, 156), (4, 117), (6, 78), (9, 52), (12, 39), (13, 36), (18, 26) So, to list all the factors of 468: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468 The negative factors of 468 would be: -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, -468 Prime Factorization of 468 To find the Prime factorization of 468, we break down all the factors of 468 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 468 only has a few differences from the above method of finding the factors of 468. 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 468: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 468. 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 468 by the smallest prime factor, in this case, 2 468 ÷ 2 = 234 2 becomes the first number in our prime factorization. Step 3: Repeat Steps 1 and 2, using 234 as the new focus. Find the smallest prime factor that isn’t 1, and divide 234 by that number. The smallest prime factor you pick for 234 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 468 are: 2, 3, 13 Find the Factors of Other Numbers Practice your factoring skills by exploring how to factor other numbers, like the ones below: Factors of 123 - The factors of 123 are 1, 3, 41, 123 Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40 Factors of 4 - The factors of 4 are 1, 2, 4 Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144