Factors of 189

Do you know that 189 can be expressed as the sum of cubes of 4 and 5? It can also be expressed as sum of cubes of 6 and (-3). In this chapter, we will calculate the factors of 189, prime factors of 189, and factors of 189 in pairs along with solved examples for a better understanding.

Factors of 189: 1, 3, 7, 9, 21, 27, 6,3 and 189
Prime Factorization of 189: 189 = 3 × 3 × 3 × 7 = 3³ × 7

1.	What Are the Factors of 189?
2.	How to Calculate Factors of 189?
3.	Factors of 189 by Prime Factorization
4.	Factors of 189 in Pairs
5.	FAQs on Factors of 189

What Are the Factors of 189?

The factors of 189 are the numbers which on multiplication give the product as 189. In other words, factors of 189 are numbers which leave no remainder when 189 is divided by them. So, when any two whole numbers are multiplied with each other and 189 is obtained as the answer, it is said that both these numbers are the factors of 189.

How to Calculate the Factors of 189?

To calculate the factors of 189, we find all the numbers which would divide 189 without leaving any remainder. 189 can be expressed as a product of its prime factors in the prime factorization method and hence we divide 189 with its divisors in the division method. For the numbers which divide 189 entirely, the divisors, as well as their quotients, are the factors of 189.

Numbers dividing 189	Factors of 189
189/1 = 189	1 and 189 are factors of 189.
189/3 = 63	3 and 63 are factors of 189.
189/7 = 27	7 and 27 are factors of 189.
189/9 = 21	9 and 21 are factors of 189.

Hence, the factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189.

Explore factors using illustrations and interactive examples.

Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
Factors of 196 - The factors of 196 are 1, 2, 4, 7, 14, 14, 28, 49, 98, and 196.
Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Factors of 189 by Prime Factorization

When a composite number is expressed as the product of its prime factors, it is known as prime factorization.
To get the prime factorization of 189, we use two methods:

Method 1: Factor Tree Method
Method 2: Upside-Down Division Method

Method 1: Factor Tree Method

The factor tree for 189 is:

Factor Tree of 189

Method 2: Upside-Down Division Method

On dividing 189 by its smallest prime factor which is 3, we get

189/3 = 63

63 is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1. The prime factorization of 189 is shown as:

Prime Factorization of 189

Hence, the prime factors of 189 are 3 and 7. The prime factorization of 189 is 3 × 3 × 3 × 7.

Factors of 189 in Pairs

The pairs of numbers which on multiplication give 189 are the factor pairs of 189. Observe the following factors of 189 in pairs. If we consider negative integers, then the numbers in the pair factors will be negative as ( - ve × - ve ) = +ve.

Positive pair factors of 189 are: (1, 189), (3, 63), (7, 27), (9, 21)
Negative pair factors of 189 are: (-1, -189), (-3, -63), (-7, -27), (-9, -21)

Important Notes:

As the sum of digits of 189 is 18, 3 and 9 are the factors of 189.
189 is a non-perfect square number. Hence, it has even number of factors.

Example 1: Andy has to determine whether 189 and 188 have any common factors. Help him find them.

Solution:

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189.
The factors of 188 are 1, 2, 4, 47, 94, and 188.

Hence, the common factor of 189 and 188 is 1.
Example 2: Can you determine whether 13 a factor of 189 or not?

Solution:

For finding whether 13 is a factor of 189 or not, we need to divide 189 by 13.
On dividing 189 by 13 we get 14 as the quotient and 7 as the remainder. This shows that 189 is not entirely divisible by 13.

Hence, 13 is not a factor of 189.

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FAQs on Factors of 189

What are the factors of 189?

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

What are the prime factors of 189?

The prime factors of 189 are 3 and 7.

Are any factors of 189 perfect squares?

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189. 9 is the only factor of 189 which is a perfect square.

What are the common factors of 189 and 210?

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189. The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210. Hence, the common factors of 189 and 210 are 1, 3, 7, and 21.

Is 8 a factor of 189 ?

No, 8 is not a factor of 189.

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