What are the Factors of 784?

The following are the different types of factors of 784:

• Factors of 784: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

• Sum of Factors of 784: 1767

• Negative Factors of 784: -1, -2, -4, -7, -8, -14, -16, -28, -49, -56, -98, -112, -196, -392, -784

• Prime Factors of 784: 2, 7

• Prime Factorization of 784: 2^4 × 7^2

There are two ways to find the factors of 784: using factor pairs, and using prime factorization.

Factor pairs of 784 are any two numbers that, when multiplied together, equal 784. The question to ask is “what two numbers multiplied together equal 784?” Every factor can be paired with another factor, and multiplying the two will result in 784.

To find the factor pairs of 784, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 784. 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 784 by the smallest prime factor, in this case, 2:

784 ÷ 2 = 392

2 and 392 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 392 as the new focus. Find the smallest prime factor that isn’t 1, and divide 392 by that number. In this case, 2 is the new smallest prime factor:

392 ÷ 2 = 196

Remember that this new factor pair is only for the factors of 392, not 784. So, to finish the factor pair for 784, you’d multiply 2 and 2 before pairing with 196:

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 784:

(1, 784), (2, 392), (4, 196), (7, 112), (8, 98), (14, 56), (16, 49), (28, 28)

So, to list all the factors of 784: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784

The negative factors of 784 would be: -1, -2, -4, -7, -8, -14, -16, -28, -49, -56, -98, -112, -196, -392, -784

To find the Prime factorization of 784, we break down all the factors of 784 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 784 only has a few differences from the above method of finding the factors of 784. 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 784:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 784. 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 784 by the smallest prime factor, in this case, 2

784 ÷ 2 = 392

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 392 as the new focus. Find the smallest prime factor that isn’t 1, and divide 392 by that number. The smallest prime factor you pick for 392 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 784 are: 2, 7

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 95 - The factors of 95 are 1, 5, 19, 95

Factors of 63 - The factors of 63 are 1, 3, 7, 9, 21, 63

Factors of 87 - The factors of 87 are 1, 3, 29, 87

Factors of 133 - The factors of 133 are 1, 7, 19, 133