191 LearnersLast updated on May 26th, 2025
Factors of 189
Factors are the numbers which can divide the number without leaving any remainder. In real life, we use factors for distributing any items equally in a group or for comparing and so on. Let's learn more about factors of 189.
What are the Factors of 189?
The factors of 189 are the numbers that divide 189 exactly without leaving any remainder. The numbers 1, 3, 7, 9, 21, 27, 63, and 189 are the factors of 189.
Negative Factors of 189: Negative factors are the opposite of positive factors. For 189, they are -1, -3, -7, -9, -21, -27, -63, and -189.
Prime Factors of 189: The prime numbers of 189 are 3 and 7, as it is the only prime number that divides it evenly without any remainder.
Prime Factorization of 189: Prime factorization is the breakdown of a number into its prime factors. For 189, the prime factor is 33 × 7
How to Find the Factors of 189
We can find the factors by dividing the number completely or by using its factors. The following are the ways by which we can find the factors
Finding Factors using Multiplication
In this method, we will try to find such pairs of numbers, in which the product of the pair would give the original number as the result. We should follow the steps mentioned below to find the factors.
Step 1 : Identify a pair of numbers whose product equals 189.
Step 2 : List such pairs of numbers one by one.
Here, the factor pairs of 189 are (1, 189), (3, 63), (7, 27), and (9, 21).
Finding Factors by Division Method
In the division method, we need to find such numbers that will divide a number evenly without leaving any remainder.
189 ÷ 1 = 189
189 ÷ 3 = 63
189 ÷ 7 = 27
189 ÷ 9 = 21
189 ÷ 21 = 9
189 ÷ 27 = 7
189 ÷ 63 = 3
189 ÷ 189 = 1
To find the factors of 189 using the division method, 189 is first divided by 1 and continues upon. The numbers 1, 3, 7, 9, 21, 27, 63, and 189 are the factors of 189.
Prime Factors and Prime Factorization
In the method of prime factorization, a number is expressed as a product of its prime factors. For example, 189 is expressed as 33 × 7. Here, 3 and 7 are the prime numbers that would divide 189 evenly. Hence, they are called the prime factors of 189.
Factor Tree:
A factor tree is a diagrammatic representation that breaks down the prime factors of the given number.
Factor Pairs:
The factor pairs of a number refer to the pairs of numbers which, when multiplied, will give the original number as a product.
Positive pair factors of 189 are (1, 189), (3, 63), (7, 27), and (9, 21).
Negative pair factors of 189 are (-1, -189), (-3, -63), (-7, -27), and (-9, -21).
Common Mistakes and How to Avoid Them in Factors of 189
Children make mistakes while finding factors. So, they need to avoid making mistakes by being careful. And, some common mistakes made by children are given below :
Mistake 1
.A child might consider only one of the numbers among the factor pair and miss out on the other number.
A child must list all the factor pairs first, i.e. (1, 189), (3, 63), ....and then write the factors individually, i.e., 1, 3, 7, 9,……189
Factors of 189 Examples
Problem 1
The area of a rectangle is 189 square units. If the length is 21 units, then what is the measure of its width?
Area of rectangle: 189 sq units
Factors of 189: 1, 3, 7, 9, 21, 27, 63, and 189.
We know that the area of a rectangle is the product of its length and breadth.
Given, length= 21 units
The factor pair of 189 is (9,21). Hence, the length is 21 units. Let’s check it through the formula for area.
So, length × width = area
⇒ 21 × width = 189
⇒ width = 189/21 = 9.
Answer: 9 units
Explanation
Here the concept of factor pairs for 189 is used and rechecked using the formula for finding the area of a rectangle.
Problem 2
What is the GCF of 189 and 225?
Factors of 189 = 1, 3, 7, 9, 21, 27, 63, and 189.
Factors of 225 = 1, 3, 5, 9, 15, 25, 45, 75, and 225
The Common Factors of 189 and 225 are 1, 3, and 9
Therefore, the GCF of 189 and 225 is 9
Explanation
List down the common factors from 189 and 225 and then find the larger number among both, so the GCF of 189 and 225 is 9.
Problem 3
If a number is divisible by both 3 and 63, is it divisible by 189?
Yes, any number which is divisible by 3 and 63 is also divisible by 189, because 189 is the product of 3 and 63
Explanation
Any number which is divisible by the factor 3 and factor 63 of 189, then it is also divisible by 189, hence 189 is a product of 63 and 3.
FAQs on Factors of 189
1.Express 189 mean in words?
2.How many divisors does 189 have?
3.Is 189 a natural number?
4. GCF of 189 and 66 will be?
5. Is 189 a multiple of 7?
6.How can children in Canada use numbers in everyday life to understand Factors of 189 ?
7.What are some fun ways kids in Canada can practice Factors of 189 with numbers?
8.What role do numbers and Factors of 189 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 189 skills?
Important Glossaries for Factors of 189
- Prime Numbers: The numbers that have only 2 factors 1 & the number itself are called Prime Numbers. For example: If we take the number 3, we will get the prime factorization of 1 × 3, therefore it is a prime number.
- Composite Numbers: composite numbers are the numbers that have more than 2 factors. For example: The composite number of 10 is 1, 2, 5, and 10
- Negative Factors: These numbers are the negative counterparts of the positive factors of a number. For example: the negative factor of 10 is, -1, -2, -5, -10.
- Factor Tree: A factor tree is a graphical representation of breaking down a composite number into prime factors.
- Multiple: In mathematics, a multiple means the number which can be divisible by another number without leaving any remainder. For example: 4 × 1 = 4
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About BrightChamps in Canada
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
