1. Steps to find factors of 738 using Division Method

Example: Find factors of 738

  • Divide 738 by 1: 738 ÷ 1 : Remainder = 0
  • Divide 738 by 2: 738 ÷ 2 : Remainder = 0
  • Divide 738 by 3: 738 ÷ 3 : Remainder = 0
  • Divide 738 by 6: 738 ÷ 6 : Remainder = 0
  • Divide 738 by 9: 738 ÷ 9 : Remainder = 0
  • Divide 738 by 18: 738 ÷ 18 : Remainder = 0
  • Divide 738 by 41: 738 ÷ 41 : Remainder = 0
  • Divide 738 by 82: 738 ÷ 82 : Remainder = 0
  • Divide 738 by 123: 738 ÷ 123 : Remainder = 0
  • Divide 738 by 246: 738 ÷ 246 : Remainder = 0
  • Divide 738 by 369: 738 ÷ 369 : Remainder = 0
  • Divide 738 by 738: 738 ÷ 738 : Remainder = 0

Hence, Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, and 738

2. Steps to find factors of 738 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 738 using the division method, follow these steps:

  • Step 1. Start dividing 738 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 738, which is 2. Divide 738 by 2 to obtain the quotient (369).
    738 ÷ 2 = 369
  • Step 3. Repeat step 1 with the obtained quotient (369).
    369 ÷ 3 = 123
    123 ÷ 3 = 41
    41 ÷ 41 = 1

So, the prime factorization of 738 is, 738 = 2 x 3 x 3 x 41.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 738 as shown below:

So, the prime factorization of 738 is, 738 = 2 x 3 x 3 x 41.

3. Find factors of 738 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 738 would be the two numbers which, when multiplied, give 738 as the result.

The following table represents the calculation of factors of 738 in pairs:

Factor Pair Pair Factorization
1 and 738 1 x 738 = 738
2 and 369 2 x 369 = 738
3 and 246 3 x 246 = 738
6 and 123 6 x 123 = 738
9 and 82 9 x 82 = 738
18 and 41 18 x 41 = 738

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 738. They are called negative pair factors.

Hence, the negative pairs of 738 would be ( -1 , -738 ) , ( -2 , -369 ) , ( -3 , -246 ) , ( -6 , -123 ) , ( -9 , -82 ) and ( -18 , -41 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 738 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, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738 are exact divisors of 738.
  • 1 is a factor of every number. Eg. 1 is a factor of 738.
  • Every number is a factor of zero (0), since 738 x 0 = 0.

Frequently Asked Questions

  • Which is the smallest prime factor of 738?

    Smallest prime factor of 738 is 2.

  • Is 738 a perfect square?

    No 738 is not a perfect square.

  • What are five multiples of 738?

    First five multiples of 738 are 1476, 2214, 2952, 3690, 4428.

  • What is prime factorization of 738?

    Prime factorization of 738 is 2 x 3 x 3 x 41.

  • What are factors of 738?

    Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.

  • How do you find factors of a negative number? ( eg. -738 )?

    Factors of -738 are -1, -2, -3, -6, -9, -18, -41, -82, -123, -246, -369, -738.

  • Is 738 a whole number?

    Yes 738 is a whole number.

  • Which is greatest factor of 738?

    The greatest factor of 738 is 369.

  • What are the prime factors of 738?

    The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.
    Prime factors of 738 are 2, 3, 3, 41.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 738. Can you help her?

Prime factors of 738 are 2, 3, 3, 41.
Hence, the product of prime factors of 246.

Can you help Rubel to find out the product of the even factors of 738?

Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.
Even factors of 738 are 2, 6, 18, 82, 246, 738.
Hence, product of even factors of 738 is; 2 x 6 x 18 x 82 x 246 x 738 = 3215578176.

Joy wants to calculate mean of all the factors of 738. Help him in finding the mean of 738.

Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 738 is 1 + 2 + 3 + 6 + 9 + 18 + 41 + 82 + 123 + 246 + 369 + 738 = 1638.
Hence, the mean of factors of 738 is 1638 ÷ 12 = 136.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 738? Help her in writing all the factors.

Positive factors are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.
Negative factors are -1, -2, -3, -6, -9, -18, -41, -82, -123, -246, -369, -738.

How many factors are there for 738?

Factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738.
So there are in total 12 factors.

Joey wants to write all the prime factors of 738 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 738 are 2, 3, 3, 41.
So in exponential form it can be written as 2 x 32 x 41.

Kevin has been asked to write 11 factor(s) of 738. Can you predict the answer?

11 factor(s) of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369.