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Factors of 784

Factors of 784 are the list of integers that can be evenly divided into 784. There are overall 15 factors of 784, of which 2, 7 are its prime factors. The Prime Factorization of 784 is 24 × 72.

  • All Factors of 784: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392 and 784
  • Prime Factors of 784: 2, 7
  • Prime Factorization of 784: 24 × 72
  • Sum of Factors of 784: 1767
1. What Are the Factors of 784?
2. Factors of 784 by Prime Factorization
3. Factors of 784 in Pairs
4. FAQs on Factors of 784
Factors of 784

What are Factors of 784?

Factors of 784 are pairs of those numbers whose products result in 784. These factors are either prime numbers or composite numbers.

How to Find the Factors of 784?

To find the factors of 784, we will have to find the list of numbers that would divide 784 without leaving any remainder.

  • 784/98 = 8; therefore, 98 is a factor of 784 and 8 is also a factor of 784.
  • 784/196 = 4; therefore, 196 is a factor of 784 and 4 is also a factor of 784.
Similarly we can find other factors. Hence, the factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.

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Factors of 784 by Prime Factorization

The number 784 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 784. The first step is to divide the number 784 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 784 ÷ 2 = 392
  • 392 ÷ 2 = 196
  • 196 ÷ 2 = 98
  • 98 ÷ 2 = 49

Further dividing 49 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 49 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 784 can be written as 24 × 72 where 2, 7 are prime.

 

Factors of 784 in Pairs

Pair factors of 784 are the pairs of numbers that when multiplied give the product 784. The factors of 784 in pairs are:

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

Negative pair factors of 784 are:

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

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 784 Solved Examples

  1. Example 1: How many factors are there for 784?

    Solution:

    The factors of 784 are too many, therefore if we can find the prime factorization of 784, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 784 = 24 × 72
    Therefore, the total number of factors are (4 + 1) × (2 + 1) = 5 × 3 = 15

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 784 and 746.

    Solution:

    The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784 and factors of 746 are 1, 2, 373, 746.

    Therefore, the Least Common Multiple (LCM) of 784 and 746 is 292432 and Greatest Common Divisor (GCD) of 784 and 746 is 2.

  3. Example 3: Find if 1, 2, 4, 7, 56, 112, 596 and 784 are factors of 784.

    Solution:

    When we divide 784 by 596 it leaves a remainder. Therefore, the number 596 is not a factor of 784. All numbers except 596 are factors of 784.

  4. Example 4: Find the product of all the prime factors of 784.

    Solution:

    Since, the prime factors of 784 are 2, 7. Therefore, the product of prime factors = 2 × 7 = 14.

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FAQs on Factors of 784

What are the Factors of 784?

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784 and its negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -49, -56, -98, -112, -196, -392, -784.

What is the Sum of all Factors of 784?

Sum of all factors of 784 = (24 + 1 - 1)/(2 - 1) × (72 + 1 - 1)/(7 - 1) = 1767

What are Prime Factors of 784?

The prime factors of 784 are 2, 7.

What is the Greatest Common Factor of 784 and 764?

The factors of 784 and 764 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784 and 1, 2, 4, 191, 382, 764 respectively.

Common factors of 784 and 764 are [1, 2, 4].

Hence, the GCF of 784 and 764 is 4.

What are the Common Factors of 784 and 691?

Since, the factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784 and factors of 691 are 1, 691. Hence, 784 and 691 have only one common factor which is 1. Therefore, 784 and 691 are co-prime.

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