1. Steps to find factors of 735 using Division Method

Example: Find factors of 735

  • Divide 735 by 1: 735 ÷ 1 : Remainder = 0
  • Divide 735 by 3: 735 ÷ 3 : Remainder = 0
  • Divide 735 by 5: 735 ÷ 5 : Remainder = 0
  • Divide 735 by 7: 735 ÷ 7 : Remainder = 0
  • Divide 735 by 15: 735 ÷ 15 : Remainder = 0
  • Divide 735 by 21: 735 ÷ 21 : Remainder = 0
  • Divide 735 by 35: 735 ÷ 35 : Remainder = 0
  • Divide 735 by 49: 735 ÷ 49 : Remainder = 0
  • Divide 735 by 105: 735 ÷ 105 : Remainder = 0
  • Divide 735 by 147: 735 ÷ 147 : Remainder = 0
  • Divide 735 by 245: 735 ÷ 245 : Remainder = 0
  • Divide 735 by 735: 735 ÷ 735 : Remainder = 0

Hence, Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, and 735

2. Steps to find factors of 735 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 735 using the division method, follow these steps:

  • Step 1. Start dividing 735 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 735, which is 3. Divide 735 by 3 to obtain the quotient (245).
    735 ÷ 3 = 245
  • Step 3. Repeat step 1 with the obtained quotient (245).
    245 ÷ 5 = 49
    49 ÷ 7 = 7
    7 ÷ 7 = 1

So, the prime factorization of 735 is, 735 = 3 x 5 x 7 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 735 as shown below:

So, the prime factorization of 735 is, 735 = 3 x 5 x 7 x 7.

3. Find factors of 735 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 735 would be the two numbers which, when multiplied, give 735 as the result.

The following table represents the calculation of factors of 735 in pairs:

Factor Pair Pair Factorization
1 and 735 1 x 735 = 735
3 and 245 3 x 245 = 735
5 and 147 5 x 147 = 735
7 and 105 7 x 105 = 735
15 and 49 15 x 49 = 735
21 and 35 21 x 35 = 735

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 735. They are called negative pair factors.

Hence, the negative pairs of 735 would be ( -1 , -735 ) , ( -3 , -245 ) , ( -5 , -147 ) , ( -7 , -105 ) , ( -15 , -49 ) and ( -21 , -35 ) .

What are factors?

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

Properties of factors

  • Every number is a factor of zero (0), since 735 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, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735 are exact divisors of 735.
  • Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735. Each factor divides 735 without leaving a remainder.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -735 )?

    Factors of -735 are -1, -3, -5, -7, -15, -21, -35, -49, -105, -147, -245, -735.

  • What is the sum of all factors of 735?

    The sum of all factors of 735 is 1368.

  • What is prime factorization of 735?

    Prime factorization of 735 is 3 x 5 x 7 x 7.

  • What are the pair factors of 735?

    Pair factors of 735 are (1,735), (3,245), (5,147), (7,105), (15,49), (21,35).

  • What are six multiples of 735?

    First five multiples of 735 are 1470, 2205, 2940, 3675, 4410, 5145.

  • Is 735 a whole number?

    Yes 735 is a whole number.

  • Which is the smallest prime factor of 735?

    Smallest prime factor of 735 is 3.

  • What are five multiples of 735?

    First five multiples of 735 are 1470, 2205, 2940, 3675, 4410.

  • Write all factors of 735?

    Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.

Examples of Factors

Joey wants to write all the prime factors of 735 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 735 are 3, 5, 7, 7.
So in exponential form it can be written as 3 x 5 x 72.

How many factors are there for 735?

Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 735. Can you predict the answer?

11 factor(s) of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245.

Sammy is puzzled while calculating the prime factors of 735. Can you help him find them?

Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
Prime factors of 735 are 3, 5, 7, 7

What is prime factorization of 735?

Prime factorization of 735 is 3 x 5 x 7 x 7 = 3 x 5 x 72.

Ariel has been assigned the task to find the product of all the prime factors of 735. Can you help her?

Prime factors of 735 are 3, 5, 7, 7.
Hence, the product of prime factors of 105.

Can you help Rubel to find out the product of the even factors of 735?

Factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735.
Even factors of 735 are 0.
Hence, product of even factors of 735 is; 0 = 0.