Q:

What are the Factors of 143?

Accepted Solution

A:
Factors of 143 Methods What are the Factors of 143? The following are the different types of factors of 143: • Factors of 143: 1, 11, 13, 143 • Sum of Factors of 143: 168 • Negative Factors of 143: -1, -11, -13, -143 • Prime Factors of 143: 11, 13 • Prime Factorization of 143: 11^1 × 13^1 There are two ways to find the factors of 143: using factor pairs, and using prime factorization. The Factor Pairs of 143 Factor pairs of 143 are any two numbers that, when multiplied together, equal 143. The question to ask is “what two numbers multiplied together equal 143?” Every factor can be paired with another factor, and multiplying the two will result in 143. To find the factor pairs of 143, follow these steps: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 143. 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 11. Step 2: Divide 143 by the smallest prime factor, in this case, 11: 143 ÷ 11 = 13 11 and 13 will make a new factor pair. Step 3: Repeat Steps 1 and 2, using 13 as the new focus. Find the smallest prime factor that isn’t 1, and divide 13 by that number. In this case, 13 is the new smallest prime factor: 13 ÷ 13 = 1 Remember that this new factor pair is only for the factors of 13, not 143. So, to finish the factor pair for 143, you’d multiply 11 and 13 before pairing with 1: 11 x 13 = 143 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 143: (1, 143), (11, 13) So, to list all the factors of 143: 1, 11, 13, 143 The negative factors of 143 would be: -1, -11, -13, -143 Prime Factorization of 143 To find the Prime factorization of 143, we break down all the factors of 143 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 143 only has a few differences from the above method of finding the factors of 143. 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 143: Step 1: Find the smallest prime number that is larger than 1, and is a factor of 143. 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 11. Step 2: Divide 143 by the smallest prime factor, in this case, 11 143 ÷ 11 = 13 11 becomes the first number in our prime factorization. Step 3: Repeat Steps 1 and 2, using 13 as the new focus. Find the smallest prime factor that isn’t 1, and divide 13 by that number. The smallest prime factor you pick for 13 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 143 are: 11, 13 Find the Factors of Other Numbers Practice your factoring skills by exploring how to factor other numbers, like the ones below: Factors of 139 - The factors of 139 are 1, 139 Factors of 51 - The factors of 51 are 1, 3, 17, 51 Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 116 - The factors of 116 are 1, 2, 4, 29, 58, 116