1. Steps to find factors of 45 using Division Method

Example: Find factors of 45

  • Divide 45 by 1: 45 ÷ 1 : Remainder = 0
  • Divide 45 by 3: 45 ÷ 3 : Remainder = 0
  • Divide 45 by 5: 45 ÷ 5 : Remainder = 0
  • Divide 45 by 9: 45 ÷ 9 : Remainder = 0
  • Divide 45 by 15: 45 ÷ 15 : Remainder = 0
  • Divide 45 by 45: 45 ÷ 45 : Remainder = 0

Hence, Factors of 45 are 1, 3, 5, 9, 15, and 45

2. Steps to find factors of 45 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 45 using the division method, follow these steps:

  • Step 1. Start dividing 45 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 45, which is 3. Divide 45 by 3 to obtain the quotient (15).
    45 ÷ 3 = 15
  • Step 3. Repeat step 1 with the obtained quotient (15).
    15 ÷ 3 = 5
    5 ÷ 5 = 1

So, the prime factorization of 45 is, 45 = 3 x 3 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 45 as shown below:

So, the prime factorization of 45 is, 45 = 3 x 3 x 5.

3. Find factors of 45 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 45 would be the two numbers which, when multiplied, give 45 as the result.

The following table represents the calculation of factors of 45 in pairs:

Factor Pair Pair Factorization
1 and 45 1 x 45 = 45
3 and 15 3 x 15 = 45
5 and 9 5 x 9 = 45

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 45. They are called negative pair factors.

Hence, the negative pairs of 45 would be ( -1 , -45 ) , ( -3 , -15 ) and ( -5 , -9 ) .

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 factor of a number is an exact divisor of that number, example 1, 3, 5, 9, 15, 45 are exact divisors of 45.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 45 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 45.

Frequently Asked Questions

  • Which is the smallest prime factor of 45?

    Smallest prime factor of 45 is 3.

  • Is 45 a perfect square?

    No 45 is not a perfect square.

  • What are five multiples of 45?

    First five multiples of 45 are 90, 135, 180, 225, 270.

  • What is prime factorization of 45?

    Prime factorization of 45 is 3 x 3 x 5.

  • What are factors of 45?

    Factors of 45 are 1, 3, 5, 9, 15, 45.

  • How do you find factors of a negative number? ( eg. -45 )?

    Factors of -45 are -1, -3, -5, -9, -15, -45.

  • Is 45 a whole number?

    Yes 45 is a whole number.

  • Which is greatest factor of 45?

    The greatest factor of 45 is 15.

  • What are the prime factors of 45?

    The factors of 45 are 1, 3, 5, 9, 15, 45.
    Prime factors of 45 are 3, 3, 5.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 45. Can you help her?

Prime factors of 45 are 3, 3, 5.
Hence, the product of prime factors of 15.

Can you help Rubel to find out the product of the even factors of 45?

Factors of 45 are 1, 3, 5, 9, 15, 45.
Even factors of 45 are 0.
Hence, product of even factors of 45 is; 0 = 0.

Joy wants to calculate mean of all the factors of 45. Help him in finding the mean of 45.

Factors of 45 are 1, 3, 5, 9, 15, 45.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 45 is 1 + 3 + 5 + 9 + 15 + 45 = 78.
Hence, the mean of factors of 45 is 78 ÷ 6 = 13.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 45? Help her in writing all the factors.

Positive factors are 1, 3, 5, 9, 15, 45.
Negative factors are -1, -3, -5, -9, -15, -45.

How many factors are there for 45?

Factors of 45 are 1, 3, 5, 9, 15, 45.
So there are in total 6 factors.

Joey wants to write all the prime factors of 45 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 45 are 3, 3, 5.
So in exponential form it can be written as 32 x 5.

Kevin has been asked to write 5 factor(s) of 45. Can you predict the answer?

5 factor(s) of 45 are 1, 3, 5, 9, 15.