173 LearnersLast updated on May 26th, 2025
Factors of 231
Factors are the numbers that divide another number equally, without leaving any remainder. When you multiply two numbers to find another number, the two which are multiplied are factors. You can think of factors as the building blocks that will help you make numbers.
What are the factors of 231?
Factors are the numbers that help us divide things equally without any leftovers. Let’s learn about the Factors of 231 which are 1, 3, 7, 11, 21, 33, 77, and 231. The number has both positive and negative integers that divide 231 without leaving any remainder.
How to find the factors of 231?
Factors help us divide numbers equally, making calculations faster and easier.Given below are the methods used to find factors:
Finding Factors Using Multiplication
In this method, we take two numbers and find the product of those two numbers to get the required number.
Example:
3×77=231
7×33=231
11 × 21=231
1 × 231=231
This means that 1, 3, 7, 11, 21, 33, 77, and 231 are the factors of 231.
Finding Factors by Division Method
We divide 231 by numbers starting from 1 and see which number gives the remainder of 0.
231 ÷ 1=231
231 ÷ 3=77
231 ÷ 7=33
231 ÷ 11=21
231 ÷ 21=21
231 ÷ 33=7
231 ÷ 77=3
231 ÷ 231=1
So the factors are 1, 3, 7, 11, 21, 33, 77, and 231.
Prime Factorization
The breaking down of numbers as prime factors is called prime factorization. The factors of 231 are:
231=3 × 7 × 11
Factor tree
A factor tree shows how a number can be parted down into prime factors.231 is broken down into two factors, 3 × 7 × 11.
Factor Pairs
Positive and negative pairs:
The factors of a number will have both the positive and negative numbers:
Positive: (1, 231), (3, 77), (7, 33), (11, 21)
Negative: (-1, -231), (-3, -77), (-7, -33), (-11, -21)
Common Mistakes and How to Avoid Them in Factors of 231
While learning about factors of 231, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
Mistake 1
Improper calculation in division
Children may get confused while performing divisions in the carry forward of numbers, which may lead to improper results. To avoid this, students should practice division to be better at the calculations.
factors of 231 Examples
Problem 1
List All the Factors of 231.
From the prime factorization, 231=3×7×11. The factors are 1,3,7,11,21,33,77,231.
Explanation
The factors of 231 include all numbers that can be formed by multiplying its prime factors. Since we found 8 different combinations, 231 has 8 factors.
Problem 2
Verify if 231 is a Composite Number.
A composite number has factors of more than two.
Factors of 231: 1,3,7,11,21,33,77,231
Since 231 has more than two factors, it is a composite number.
Explanation
231 is a composite number because it has more than just two factors (1 and 231). It has several divisors, such as 3, 7, 11, etc., confirming it is not a prime number.
Problem 3
Find the Greatest Common Factor (GCF) of 231 and 77.
Factors of 231: 1,3,7,11,21,33,77,231
Factors of 77: 1,7,11,771, 7, 11, 771,7,11,77
GCF = 77
Explanation
The GCF of 231 and 77 is 77 because it is the largest number that divides both 231 and 77 without a remainder.
FAQs on Factors of 231
1.What is the negative pair of 231?
2.What is the product of 231?
3.Is 231 a perfect square?
4.What number is 231 divisible by 7?
5.What is a factor of 231?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 231?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 231 with numbers?
8.What role do numbers and Factors of 231 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 231 skills?
Important Glossaries for Factors of [Topic]
- Prime Factorization: It is a method of splitting down a number into its factors. For example: 231=3 × 7 × 11
- Divisibility: A number is said to be divisible by a certain number, when we divide a number it should give a whole number and not a decimal.
- Even number: A number that when divided by 2 gives a whole number.
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