1. Steps to find factors of 675 using Division Method

Example: Find factors of 675

  • Divide 675 by 1: 675 ÷ 1 : Remainder = 0
  • Divide 675 by 3: 675 ÷ 3 : Remainder = 0
  • Divide 675 by 5: 675 ÷ 5 : Remainder = 0
  • Divide 675 by 9: 675 ÷ 9 : Remainder = 0
  • Divide 675 by 15: 675 ÷ 15 : Remainder = 0
  • Divide 675 by 25: 675 ÷ 25 : Remainder = 0
  • Divide 675 by 27: 675 ÷ 27 : Remainder = 0
  • Divide 675 by 45: 675 ÷ 45 : Remainder = 0
  • Divide 675 by 75: 675 ÷ 75 : Remainder = 0
  • Divide 675 by 135: 675 ÷ 135 : Remainder = 0
  • Divide 675 by 225: 675 ÷ 225 : Remainder = 0
  • Divide 675 by 675: 675 ÷ 675 : Remainder = 0

Hence, Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, and 675

2. Steps to find factors of 675 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 675 using the division method, follow these steps:

  • Step 1. Start dividing 675 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 675, which is 3. Divide 675 by 3 to obtain the quotient (225).
    675 ÷ 3 = 225
  • Step 3. Repeat step 1 with the obtained quotient (225).
    225 ÷ 3 = 75
    75 ÷ 3 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 675 is, 675 = 3 x 3 x 3 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 675 as shown below:

So, the prime factorization of 675 is, 675 = 3 x 3 x 3 x 5 x 5.

3. Find factors of 675 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 675 would be the two numbers which, when multiplied, give 675 as the result.

The following table represents the calculation of factors of 675 in pairs:

Factor Pair Pair Factorization
1 and 675 1 x 675 = 675
3 and 225 3 x 225 = 675
5 and 135 5 x 135 = 675
9 and 75 9 x 75 = 675
15 and 45 15 x 45 = 675
25 and 27 25 x 27 = 675

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 675. They are called negative pair factors.

Hence, the negative pairs of 675 would be ( -1 , -675 ) , ( -3 , -225 ) , ( -5 , -135 ) , ( -9 , -75 ) , ( -15 , -45 ) and ( -25 , -27 ) .

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 675 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, 9, 15, 25, 27, 45, 75, 135, 225, 675 are exact divisors of 675.
  • Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675. Each factor divides 675 without leaving a remainder.

Frequently Asked Questions

  • Which is the smallest prime factor of 675?

    Smallest prime factor of 675 is 3.

  • Is 675 a perfect square?

    No 675 is not a perfect square.

  • What are five multiples of 675?

    First five multiples of 675 are 1350, 2025, 2700, 3375, 4050.

  • What is prime factorization of 675?

    Prime factorization of 675 is 3 x 3 x 3 x 5 x 5.

  • What are factors of 675?

    Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.

  • How do you find factors of a negative number? ( eg. -675 )?

    Factors of -675 are -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225, -675.

  • Is 675 a whole number?

    Yes 675 is a whole number.

  • Which is greatest factor of 675?

    The greatest factor of 675 is 225.

  • What are the prime factors of 675?

    The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
    Prime factors of 675 are 3, 3, 3, 5, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 675. Can you help her?

Prime factors of 675 are 3, 3, 3, 5, 5.
Hence, the product of prime factors of 15.

Can you help Rubel to find out the product of the even factors of 675?

Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
Even factors of 675 are 0.
Hence, product of even factors of 675 is; 0 = 0.

Joy wants to calculate mean of all the factors of 675. Help him in finding the mean of 675.

Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 675 is 1 + 3 + 5 + 9 + 15 + 25 + 27 + 45 + 75 + 135 + 225 + 675 = 1240.
Hence, the mean of factors of 675 is 1240 ÷ 12 = 103.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 675? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
Negative factors are -1, -3, -5, -9, -15, -25, -27, -45, -75, -135, -225, -675.

How many factors are there for 675?

Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675.
So there are in total 12 factors.

Joey wants to write all the prime factors of 675 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 675 are 3, 3, 3, 5, 5.
So in exponential form it can be written as 33 x 52.

Kevin has been asked to write 11 factor(s) of 675. Can you predict the answer?

11 factor(s) of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225.