Last updated on May 26th, 2025
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.
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.
Factors help us divide numbers equally, making calculations faster and easier.Given below are the methods used to find factors:
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.
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.
The breaking down of numbers as prime factors is called prime factorization. The factors of 231 are:
231=3 × 7 × 11
A factor tree shows how a number can be parted down into prime factors.231 is broken down into two factors, 3 × 7 × 11.
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)
While learning about factors of 231, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
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.
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.
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.
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.
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
The GCF of 231 and 77 is 77 because it is the largest number that divides both 231 and 77 without a remainder.