1. Steps to find factors of 724 using Division Method

Example: Find factors of 724

  • Divide 724 by 1: 724 ÷ 1 : Remainder = 0
  • Divide 724 by 2: 724 ÷ 2 : Remainder = 0
  • Divide 724 by 4: 724 ÷ 4 : Remainder = 0
  • Divide 724 by 181: 724 ÷ 181 : Remainder = 0
  • Divide 724 by 362: 724 ÷ 362 : Remainder = 0
  • Divide 724 by 724: 724 ÷ 724 : Remainder = 0

Hence, Factors of 724 are 1, 2, 4, 181, 362, and 724

2. Steps to find factors of 724 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 724 using the division method, follow these steps:

  • Step 1. Start dividing 724 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 724, which is 2. Divide 724 by 2 to obtain the quotient (362).
    724 ÷ 2 = 362
  • Step 3. Repeat step 1 with the obtained quotient (362).
    362 ÷ 2 = 181
    181 ÷ 181 = 1

So, the prime factorization of 724 is, 724 = 2 x 2 x 181.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 724 as shown below:

So, the prime factorization of 724 is, 724 = 2 x 2 x 181.

3. Find factors of 724 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 724 would be the two numbers which, when multiplied, give 724 as the result.

The following table represents the calculation of factors of 724 in pairs:

Factor Pair Pair Factorization
1 and 724 1 x 724 = 724
2 and 362 2 x 362 = 724
4 and 181 4 x 181 = 724

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 724. They are called negative pair factors.

Hence, the negative pairs of 724 would be ( -1 , -724 ) , ( -2 , -362 ) and ( -4 , -181 ) .

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. 724 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 724.
  • Every number is a factor of zero (0), since 724 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, 181, 362, 724 are exact divisors of 724.
  • Factors of 724 are 1, 2, 4, 181, 362, 724. Each factor divides 724 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 181, 362, 724 are all less than or equal to 724.

Frequently Asked Questions

  • Is 724 a perfect square?

    No 724 is not a perfect square.

  • What are factors of 724?

    Factors of 724 are 1, 2, 4, 181, 362, 724.

  • Which is greatest factor of 724?

    The greatest factor of 724 is 362.

  • What is the sum of all factors of 724?

    The sum of all factors of 724 is 1274.

  • What are multiples of 724?

    First five multiples of 724 are 1448, 2172, 2896, 3620.

  • What is the greatest prime factors of 724?

    The greatest prime factor of 724 is 181.

  • What are six multiples of 724?

    First five multiples of 724 are 1448, 2172, 2896, 3620, 4344, 5068.

  • What is prime factorization of 724?

    Prime factorization of 724 is 2 x 2 x 181.

  • Is 724 a whole number?

    Yes 724 is a whole number.

Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 724? Help her in writing all the factors.

Positive factors are 1, 2, 4, 181, 362, 724.
Negative factors are -1, -2, -4, -181, -362, -724.

Can you help Sammy find out the product of the odd factors of 724?

Factors of 724 are 1, 2, 4, 181, 362, 724.
Odd factors of 724 are 1, 181.
Hence product of odd factors of 724 is; 1 x 181 = 181.

Joey wants to write all the prime factors of 724 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 724 are 2, 2, 181.
So in exponential form it can be written as 22 x 181.

How many factors are there for 724?

Factors of 724 are 1, 2, 4, 181, 362, 724.
So there are in total 6 factors.

Kevin has been asked to write 5 factor(s) of 724. Can you predict the answer?

5 factor(s) of 724 are 1, 2, 4, 181, 362.

Sammy is puzzled while calculating the prime factors of 724. Can you help him find them?

Factors of 724 are 1, 2, 4, 181, 362, 724.
Prime factors of 724 are 2, 2, 181

What is prime factorization of 724?

Prime factorization of 724 is 2 x 2 x 181 = 22 x 181.