What are the Factors of 728?

Factors of 728 Methods What are the Factors of 728? The following are the different types of factors of 728: • Factors of 728: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 • Sum of Factors of 728: 1680 • Negative Factors of 728: -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, -728 • Prime Factors of 728: 2, 7, 13 • Prime Factorization of 728: 2^3 × 7^1 × 13^1 There are two ways to find the factors of 728: using factor pairs, and using prime factorization. The Factor Pairs of 728 Factor pairs of 728 are any two numbers that, when multiplied together, equal 728. The question to ask is “what two numbers multiplied together equal 728?” Every factor can be paired with another factor, and multiplying the two will result in 728. To find the factor pairs of 728, follow these steps: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 728. 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 728 by the smallest prime factor, in this case, 2: 728 ÷ 2 = 364 2 and 364 will make a new factor pair. Step 3: Repeat Steps 1 and 2, using 364 as the new focus. Find the smallest prime factor that isn’t 1, and divide 364 by that number. In this case, 2 is the new smallest prime factor: 364 ÷ 2 = 182 Remember that this new factor pair is only for the factors of 364, not 728. So, to finish the factor pair for 728, you’d multiply 2 and 2 before pairing with 182: 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 728: (1, 728), (2, 364), (4, 182), (7, 104), (8, 91), (13, 56), (14, 52), (26, 28) So, to list all the factors of 728: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 The negative factors of 728 would be: -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, -728 Prime Factorization of 728 To find the Prime factorization of 728, we break down all the factors of 728 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 728 only has a few differences from the above method of finding the factors of 728. 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 728: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 728. 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 728 by the smallest prime factor, in this case, 2 728 ÷ 2 = 364 2 becomes the first number in our prime factorization. Step 3: Repeat Steps 1 and 2, using 364 as the new focus. Find the smallest prime factor that isn’t 1, and divide 364 by that number. The smallest prime factor you pick for 364 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 728 are: 2, 7, 13 Find the Factors of Other Numbers Practice your factoring skills by exploring how to factor other numbers, like the ones below: Factors of 87 - The factors of 87 are 1, 3, 29, 87 Factors of 38 - The factors of 38 are 1, 2, 19, 38 Factors of 138 - The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138 Factors of 59 - The factors of 59 are 1, 59