1. Steps to find factors of 165 using Division Method

Example: Find factors of 165

  • Divide 165 by 1: 165 ÷ 1 : Remainder = 0
  • Divide 165 by 3: 165 ÷ 3 : Remainder = 0
  • Divide 165 by 5: 165 ÷ 5 : Remainder = 0
  • Divide 165 by 11: 165 ÷ 11 : Remainder = 0
  • Divide 165 by 15: 165 ÷ 15 : Remainder = 0
  • Divide 165 by 33: 165 ÷ 33 : Remainder = 0
  • Divide 165 by 55: 165 ÷ 55 : Remainder = 0
  • Divide 165 by 165: 165 ÷ 165 : Remainder = 0

Hence, Factors of 165 are 1, 3, 5, 11, 15, 33, 55, and 165

2. Steps to find factors of 165 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 165 using the division method, follow these steps:

  • Step 1. Start dividing 165 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 165, which is 3. Divide 165 by 3 to obtain the quotient (55).
    165 ÷ 3 = 55
  • Step 3. Repeat step 1 with the obtained quotient (55).
    55 ÷ 5 = 11
    11 ÷ 11 = 1

So, the prime factorization of 165 is, 165 = 3 x 5 x 11.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 165 as shown below:

So, the prime factorization of 165 is, 165 = 3 x 5 x 11.

3. Find factors of 165 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 165 would be the two numbers which, when multiplied, give 165 as the result.

The following table represents the calculation of factors of 165 in pairs:

Factor Pair Pair Factorization
1 and 165 1 x 165 = 165
3 and 55 3 x 55 = 165
5 and 33 5 x 33 = 165
11 and 15 11 x 15 = 165

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 165. They are called negative pair factors.

Hence, the negative pairs of 165 would be ( -1 , -165 ) , ( -3 , -55 ) , ( -5 , -33 ) and ( -11 , -15 ) .

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, 11, 15, 33, 55, 165 are exact divisors of 165.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 165 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 165.

Frequently Asked Questions

  • What are the prime factors of 165?

    The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.
    Prime factors of 165 are 3, 5, 11.

  • What two numbers make 165?

    Two numbers that make 165 are 3 and 55.

  • What is the greatest prime factors of 165?

    The greatest prime factor of 165 is 11.

  • What are factors of 165?

    Factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.

  • How do you find factors of a negative number? ( eg. -165 )?

    Factors of -165 are -1, -3, -5, -11, -15, -33, -55, -165.

  • What are five multiples of 165?

    First five multiples of 165 are 330, 495, 660, 825, 990.

  • Write some multiples of 165?

    First five multiples of 165 are 330, 495, 660, 825.

  • Is 165 a perfect square?

    No 165 is not a perfect square.

  • What two numbers make 165?

    Two numbers that make 165 are 3 and 55.

Examples of Factors

What is prime factorization of 165?

Prime factorization of 165 is 3 x 5 x 11 = 3 x 5 x 11.

Sammy is puzzled while calculating the prime factors of 165. Can you help him find them?

Factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.
Prime factors of 165 are 3, 5, 11

Kevin has been asked to write 7 factor(s) of 165. Can you predict the answer?

7 factor(s) of 165 are 1, 3, 5, 11, 15, 33, 55.

Joey wants to write all the prime factors of 165 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 165 are 3, 5, 11.
So in exponential form it can be written as 3 x 5 x 11.

How many factors are there for 165?

Factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.
So there are in total 8 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 165? Help her in writing all the factors.

Positive factors are 1, 3, 5, 11, 15, 33, 55, 165.
Negative factors are -1, -3, -5, -11, -15, -33, -55, -165.

Can you help Rubel to find out the product of the even factors of 165?

Factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.
Even factors of 165 are 0.
Hence, product of even factors of 165 is; 0 = 0.