1. Steps to find factors of 189 using Division Method

Example: Find factors of 189

  • Divide 189 by 1: 189 ÷ 1 : Remainder = 0
  • Divide 189 by 3: 189 ÷ 3 : Remainder = 0
  • Divide 189 by 7: 189 ÷ 7 : Remainder = 0
  • Divide 189 by 9: 189 ÷ 9 : Remainder = 0
  • Divide 189 by 21: 189 ÷ 21 : Remainder = 0
  • Divide 189 by 27: 189 ÷ 27 : Remainder = 0
  • Divide 189 by 63: 189 ÷ 63 : Remainder = 0
  • Divide 189 by 189: 189 ÷ 189 : Remainder = 0

Hence, Factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189

2. Steps to find factors of 189 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 189 using the division method, follow these steps:

  • Step 1. Start dividing 189 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 189, which is 3. Divide 189 by 3 to obtain the quotient (63).
    189 ÷ 3 = 63
  • Step 3. Repeat step 1 with the obtained quotient (63).
    63 ÷ 3 = 21
    21 ÷ 3 = 7
    7 ÷ 7 = 1

So, the prime factorization of 189 is, 189 = 3 x 3 x 3 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 189 as shown below:

So, the prime factorization of 189 is, 189 = 3 x 3 x 3 x 7.

3. Find factors of 189 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 189 would be the two numbers which, when multiplied, give 189 as the result.

The following table represents the calculation of factors of 189 in pairs:

Factor Pair Pair Factorization
1 and 189 1 x 189 = 189
3 and 63 3 x 63 = 189
7 and 27 7 x 27 = 189
9 and 21 9 x 21 = 189

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 189. They are called negative pair factors.

Hence, the negative pairs of 189 would be ( -1 , -189 ) , ( -3 , -63 ) , ( -7 , -27 ) and ( -9 , -21 ) .

How can we define factors?

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

Properties of factors

  • Every factor of a number is an exact divisor of that number, example 1, 3, 7, 9, 21, 27, 63, 189 are exact divisors of 189.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Each number is a factor of itself. Eg. 189 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 189.

Frequently Asked Questions

  • Which is the smallest prime factor of 189?

    Smallest prime factor of 189 is 3.

  • Is 189 a perfect square?

    No 189 is not a perfect square.

  • What are five multiples of 189?

    First five multiples of 189 are 378, 567, 756, 945, 1134.

  • What is prime factorization of 189?

    Prime factorization of 189 is 3 x 3 x 3 x 7.

  • What are factors of 189?

    Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.

  • How do you find factors of a negative number? ( eg. -189 )?

    Factors of -189 are -1, -3, -7, -9, -21, -27, -63, -189.

  • Is 189 a whole number?

    Yes 189 is a whole number.

  • Which is greatest factor of 189?

    The greatest factor of 189 is 63.

  • What are the prime factors of 189?

    The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.
    Prime factors of 189 are 3, 3, 3, 7.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 189. Can you help her?

Prime factors of 189 are 3, 3, 3, 7.
Hence, the product of prime factors of 21.

Can you help Rubel to find out the product of the even factors of 189?

Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.
Even factors of 189 are 0.
Hence, product of even factors of 189 is; 0 = 0.

Joy wants to calculate mean of all the factors of 189. Help him in finding the mean of 189.

Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 189 is 1 + 3 + 7 + 9 + 21 + 27 + 63 + 189 = 320.
Hence, the mean of factors of 189 is 320 ÷ 8 = 40.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 189? Help her in writing all the factors.

Positive factors are 1, 3, 7, 9, 21, 27, 63, 189.
Negative factors are -1, -3, -7, -9, -21, -27, -63, -189.

How many factors are there for 189?

Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189.
So there are in total 8 factors.

Joey wants to write all the prime factors of 189 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 189 are 3, 3, 3, 7.
So in exponential form it can be written as 33 x 7.

Kevin has been asked to write 7 factor(s) of 189. Can you predict the answer?

7 factor(s) of 189 are 1, 3, 7, 9, 21, 27, 63.