1. Steps to find factors of 722 using Division Method

Example: Find factors of 722

  • Divide 722 by 1: 722 ÷ 1 : Remainder = 0
  • Divide 722 by 2: 722 ÷ 2 : Remainder = 0
  • Divide 722 by 19: 722 ÷ 19 : Remainder = 0
  • Divide 722 by 38: 722 ÷ 38 : Remainder = 0
  • Divide 722 by 361: 722 ÷ 361 : Remainder = 0
  • Divide 722 by 722: 722 ÷ 722 : Remainder = 0

Hence, Factors of 722 are 1, 2, 19, 38, 361, and 722

2. Steps to find factors of 722 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 722 using the division method, follow these steps:

  • Step 1. Start dividing 722 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 722, which is 2. Divide 722 by 2 to obtain the quotient (361).
    722 ÷ 2 = 361
  • Step 3. Repeat step 1 with the obtained quotient (361).
    361 ÷ 19 = 19
    19 ÷ 19 = 1

So, the prime factorization of 722 is, 722 = 2 x 19 x 19.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 722 as shown below:

So, the prime factorization of 722 is, 722 = 2 x 19 x 19.

3. Find factors of 722 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 722 would be the two numbers which, when multiplied, give 722 as the result.

The following table represents the calculation of factors of 722 in pairs:

Factor Pair Pair Factorization
1 and 722 1 x 722 = 722
2 and 361 2 x 361 = 722
19 and 38 19 x 38 = 722

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 722. They are called negative pair factors.

Hence, the negative pairs of 722 would be ( -1 , -722 ) , ( -2 , -361 ) and ( -19 , -38 ) .

How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 722 is a factor of itself.
  • 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, 19, 38, 361, 722 are exact divisors of 722.
  • 1 is a factor of every number. Eg. 1 is a factor of 722.
  • Every number is a factor of zero (0), since 722 x 0 = 0.

Frequently Asked Questions

  • What two numbers make 722?

    Two numbers that make 722 are 2 and 361.

  • What is prime factorization of 722?

    Prime factorization of 722 is 2 x 19 x 19.

  • Write some multiples of 722?

    First five multiples of 722 are 1444, 2166, 2888, 3610.

  • Which is the smallest prime factor of 722?

    The smallest prime factor of 722 is 2.

  • Is 722 a perfect square?

    No 722 is not a perfect square.

  • What is the sum of all factors of 722?

    The sum of all factors of 722 is 1143.

  • What are factors of 722?

    Factors of 722 are 1, 2, 19, 38, 361, 722.

  • How do you find factors of a negative number? ( eg. -722 )?

    Factors of -722 are -1, -2, -19, -38, -361, -722.

  • Is 722 a whole number?

    Yes 722 is a whole number.

Examples of Factors

Joy wants to calculate mean of all the factors of 722. Help him in finding the mean of 722.

Factors of 722 are 1, 2, 19, 38, 361, 722.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 722 is 1 + 2 + 19 + 38 + 361 + 722 = 1143.
Hence, the mean of factors of 722 is 1143 ÷ 6 = 190.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 722? Help her in writing all the factors.

Positive factors are 1, 2, 19, 38, 361, 722.
Negative factors are -1, -2, -19, -38, -361, -722.

Joey wants to write all the prime factors of 722 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 722 are 2, 19, 19.
So in exponential form it can be written as 2 x 192.

Kevin has been asked to write 5 factor(s) of 722. Can you predict the answer?

5 factor(s) of 722 are 1, 2, 19, 38, 361.

Sammy is puzzled while calculating the prime factors of 722. Can you help him find them?

Factors of 722 are 1, 2, 19, 38, 361, 722.
Prime factors of 722 are 2, 19, 19

What is prime factorization of 722?

Prime factorization of 722 is 2 x 19 x 19 = 2 x 192.

Can you help Rubel to find out the product of the even factors of 722?

Factors of 722 are 1, 2, 19, 38, 361, 722.
Even factors of 722 are 2, 38, 722.
Hence, product of even factors of 722 is; 2 x 38 x 722 = 54872.