1. Steps to find factors of 784 using Division Method

Example: Find factors of 784

  • Divide 784 by 1: 784 ÷ 1 : Remainder = 0
  • Divide 784 by 2: 784 ÷ 2 : Remainder = 0
  • Divide 784 by 4: 784 ÷ 4 : Remainder = 0
  • Divide 784 by 7: 784 ÷ 7 : Remainder = 0
  • Divide 784 by 8: 784 ÷ 8 : Remainder = 0
  • Divide 784 by 14: 784 ÷ 14 : Remainder = 0
  • Divide 784 by 16: 784 ÷ 16 : Remainder = 0
  • Divide 784 by 28: 784 ÷ 28 : Remainder = 0
  • Divide 784 by 49: 784 ÷ 49 : Remainder = 0
  • Divide 784 by 56: 784 ÷ 56 : Remainder = 0
  • Divide 784 by 98: 784 ÷ 98 : Remainder = 0
  • Divide 784 by 112: 784 ÷ 112 : Remainder = 0
  • Divide 784 by 196: 784 ÷ 196 : Remainder = 0
  • Divide 784 by 392: 784 ÷ 392 : Remainder = 0
  • Divide 784 by 784: 784 ÷ 784 : Remainder = 0

Hence, Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, and 784

2. Steps to find factors of 784 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 784 using the division method, follow these steps:

  • Step 1. Start dividing 784 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 784, which is 2. Divide 784 by 2 to obtain the quotient (392).
    784 ÷ 2 = 392
  • Step 3. Repeat step 1 with the obtained quotient (392).
    392 ÷ 2 = 196
    196 ÷ 2 = 98
    98 ÷ 2 = 49
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 784 is, 784 = 2 x 2 x 2 x 2 x 7 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 784 as shown below:

So, the prime factorization of 784 is, 784 = 2 x 2 x 2 x 2 x 7 x 7.

3. Find factors of 784 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 784 would be the two numbers which, when multiplied, give 784 as the result.

The following table represents the calculation of factors of 784 in pairs:

Factor Pair Pair Factorization
1 and 784 1 x 784 = 784
2 and 392 2 x 392 = 784
4 and 196 4 x 196 = 784
7 and 112 7 x 112 = 784
8 and 98 8 x 98 = 784
14 and 56 14 x 56 = 784
16 and 49 16 x 49 = 784
28 and 28 28 x 28 = 784

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 784. They are called negative pair factors.

Hence, the negative pairs of 784 would be ( -1 , -784 ) , ( -2 , -392 ) , ( -4 , -196 ) , ( -7 , -112 ) , ( -8 , -98 ) , ( -14 , -56 ) , ( -16 , -49 ) and ( -28 , -28 ) .

How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

Properties of factors

  • Each number is a factor of itself. Eg. 784 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 784.
  • Every number is a factor of zero (0), since 784 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784 are exact divisors of 784.
  • Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784. Each factor divides 784 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784 are all less than or equal to 784.

Frequently Asked Questions

  • What are the prime factors of 784?

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

  • What is the sum of all factors of 784?

    The sum of all factors of 784 is 1767.

  • What are the pair factors of 784?

    Pair factors of 784 are (1,784), (2,392), (4,196), (7,112), (8,98), (14,56), (16,49), (28,28).

  • What two numbers make 784?

    Two numbers that make 784 are 2 and 392.

  • What are multiples of 784?

    First five multiples of 784 are 1568, 2352, 3136, 3920.

  • Is 784 a perfect square?

    Yes 784 is a perfect square.

  • Which is greatest factor of 784?

    The greatest factor of 784 is 392.

  • How do you factors of 784?

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

  • What are five multiples of 784?

    First five multiples of 784 are 1568, 2352, 3136, 3920, 4704.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 784?

Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
Even factors of 784 are 2, 4, 8, 14, 16, 28, 56, 98, 112, 196, 392, 784.
Hence, product of even factors of 784 is; 2 x 4 x 8 x 14 x 16 x 28 x 56 x 98 x 112 x 196 x 392 x 784 = 14861968965709595000.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 784? Help her in writing all the factors.

Positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
Negative factors are -1, -2, -4, -7, -8, -14, -16, -28, -49, -56, -98, -112, -196, -392, -784.

How many factors are there for 784?

Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
So there are in total 15 factors.

Sammy is puzzled while calculating the prime factors of 784. Can you help him find them?

Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
Prime factors of 784 are 2, 2, 2, 2, 7, 7

Joey wants to write all the prime factors of 784 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 784 are 2, 2, 2, 2, 7, 7.
So in exponential form it can be written as 24 x 72.

What is prime factorization of 784?

Prime factorization of 784 is 2 x 2 x 2 x 2 x 7 x 7 = 24 x 72.

Can you help Rubel to find out the product of the even factors of 784?

Factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
Even factors of 784 are 2, 4, 8, 14, 16, 28, 56, 98, 112, 196, 392, 784.
Hence, product of even factors of 784 is; 2 x 4 x 8 x 14 x 16 x 28 x 56 x 98 x 112 x 196 x 392 x 784 = 14861968965709595000.