1. Steps to find factors of 736 using Division Method

Example: Find factors of 736

  • Divide 736 by 1: 736 ÷ 1 : Remainder = 0
  • Divide 736 by 2: 736 ÷ 2 : Remainder = 0
  • Divide 736 by 4: 736 ÷ 4 : Remainder = 0
  • Divide 736 by 8: 736 ÷ 8 : Remainder = 0
  • Divide 736 by 16: 736 ÷ 16 : Remainder = 0
  • Divide 736 by 23: 736 ÷ 23 : Remainder = 0
  • Divide 736 by 32: 736 ÷ 32 : Remainder = 0
  • Divide 736 by 46: 736 ÷ 46 : Remainder = 0
  • Divide 736 by 92: 736 ÷ 92 : Remainder = 0
  • Divide 736 by 184: 736 ÷ 184 : Remainder = 0
  • Divide 736 by 368: 736 ÷ 368 : Remainder = 0
  • Divide 736 by 736: 736 ÷ 736 : Remainder = 0

Hence, Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, and 736

2. Steps to find factors of 736 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 736 using the division method, follow these steps:

  • Step 1. Start dividing 736 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 736, which is 2. Divide 736 by 2 to obtain the quotient (368).
    736 ÷ 2 = 368
  • Step 3. Repeat step 1 with the obtained quotient (368).
    368 ÷ 2 = 184
    184 ÷ 2 = 92
    92 ÷ 2 = 46
    46 ÷ 2 = 23
    23 ÷ 23 = 1

So, the prime factorization of 736 is, 736 = 2 x 2 x 2 x 2 x 2 x 23.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 736 as shown below:

So, the prime factorization of 736 is, 736 = 2 x 2 x 2 x 2 x 2 x 23.

3. Find factors of 736 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 736 would be the two numbers which, when multiplied, give 736 as the result.

The following table represents the calculation of factors of 736 in pairs:

Factor Pair Pair Factorization
1 and 736 1 x 736 = 736
2 and 368 2 x 368 = 736
4 and 184 4 x 184 = 736
8 and 92 8 x 92 = 736
16 and 46 16 x 46 = 736
23 and 32 23 x 32 = 736

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 736. They are called negative pair factors.

Hence, the negative pairs of 736 would be ( -1 , -736 ) , ( -2 , -368 ) , ( -4 , -184 ) , ( -8 , -92 ) , ( -16 , -46 ) and ( -23 , -32 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 736 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 736.
  • Every number is a factor of zero (0), since 736 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, 8, 16, 23, 32, 46, 92, 184, 368, 736 are exact divisors of 736.
  • Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736. Each factor divides 736 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736 are all less than or equal to 736.

Frequently Asked Questions

  • Which is the smallest prime factor of 736?

    The smallest prime factor of 736 is 2.

  • Is 736 a whole number?

    Yes 736 is a whole number.

  • What are the prime factors of 736?

    The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
    Prime factors of 736 are 2, 2, 2, 2, 2, 23.

  • What two numbers make 736?

    Two numbers that make 736 are 2 and 368.

  • What are multiples of 736?

    First five multiples of 736 are 1472, 2208, 2944, 3680.

  • What is the sum of all factors of 736?

    The sum of all factors of 736 is 1512.

  • What are five multiples of 736?

    First five multiples of 736 are 1472, 2208, 2944, 3680, 4416.

  • Is 736 a perfect square?

    No 736 is not a perfect square.

  • What is the greatest prime factors of 736?

    The greatest prime factor of 736 is 23.

Examples of Factors

How many factors are there for 736?

Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 736. Can you predict the answer?

11 factor(s) of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368.

Sammy is puzzled while calculating the prime factors of 736. Can you help him find them?

Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
Prime factors of 736 are 2, 2, 2, 2, 2, 23

What is prime factorization of 736?

Prime factorization of 736 is 2 x 2 x 2 x 2 x 2 x 23 = 25 x 23.

Ariel has been assigned the task to find the product of all the prime factors of 736. Can you help her?

Prime factors of 736 are 2, 2, 2, 2, 2, 23.
Hence, the product of prime factors of 46.

Can you help Rubel to find out the product of the even factors of 736?

Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
Even factors of 736 are 2, 4, 8, 16, 32, 46, 92, 184, 368, 736.
Hence, product of even factors of 736 is; 2 x 4 x 8 x 16 x 32 x 46 x 92 x 184 x 368 x 736 = 6910970672709632.

Joy wants to calculate mean of all the factors of 736. Help him in finding the mean of 736.

Factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 736 is 1 + 2 + 4 + 8 + 16 + 23 + 32 + 46 + 92 + 184 + 368 + 736 = 1512.
Hence, the mean of factors of 736 is 1512 ÷ 12 = 126.00.