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237 LearnersLast updated on December 10th, 2024
Factors of 21
Numbers whose dividend is completely divisible by quotient are its factors. In real life, factors are helpful in scenarios like packing boxes and arranging seats. In this article, we will be studying examples, mistakes, and methods to solve factors of 21.
What are the Factors of 21
The factors of 21 are 1, 3, 7 and 21
Negative Factors- These are negative counterparts of the positive factors.
Negative factors: -1, -3, -7, -21
Prime Factors - Prime factors are the prime numbers themselves, when multiplied together, give 21 as the product.
Prime factor: 3, 7
Prime Factorization- Prime factorization involves breaking 21 into its prime factors
It is expressed as 31 × 71
Table listing the factors of 21
|
Positive Factors |
1, 3, 7, 21 |
|
Negative Factors |
-1, -3, -7, -21 |
|
Prime Factors |
3,7 |
|
Prime Factorization |
31 × 71 |
How to Find the Factors of 21
There are different methods to find the factors of 21.
Methods to find the factors of 21:
- Multiplication Method
- Division Method
- Prime Factor and Prime Factorization
- Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 21 as their product.
Step-by-step process
Step 1: Find the pair of numbers whose product is 21.
Step 2: The factors are those numbers, when multiplied, give 21.
Step 3: Make a list of numbers whose product will be 21.
A list of numbers whose products are 21 is given below:
1 × 21 = 21
3 × 7 = 21
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number.
Step-by-step process
Step 1: Since every number is divisible by 1, 1 will always be a factor. Example: 21÷1 = 21
Step 2: Move to the next integer. Both divisor and quotient are the factors.
Overview of Factors of 21 using the division method
Prime Factors and Prime Factorization
Prime Factors of 21-There is only one prime factor for 21
Prime factors of 21: 3, 7
Steps to find the prime factors of 21
Step 1: Divide 21 using the prime number 3
21÷3 = 7
Step 2: Divide 5 with the prime number 7
7÷7 = 1
Prime Factorization of 21- Prime Factorization breaks down the prime factors of 21
Expressed as 31 × 71
Factor Tree
The prime factorization is visually represented using the factor tree. It helps to understand the process easily. In this factor tree, each branch splits into prime factors.
Factor Tree for 21:
Factors of 10 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.
Positive Factor Pairs: (1,21), (3,7)
Negative Factor Pairs: (-1,-21), (-3,-7)
Common Mistakes and How to Avoid Them in Factors of 21
Factors of 21, examples
Problem 1
Can you express 21 as a product of two factors other than 1 and 21?
Explanation
Problem 2
What is the sum of factors of 21?
Explanation
Problem 3
Identify the factor pair whose sum is 10
Explanation
FAQs on Factors of 21
1.Does 21 only have 2 factors?
2.Is 21 a prime factor?
3.What is the factor tree of 21?
4.Is 18 a factor of 21?
5.Is 21 a factor of 28?
Important glossaries for the Factors of 21
- Divisor: Number that divides another number
- Quotient: The number you get when you divide a number with another.
- Factors: Numbers that divide the given number, leaving zero as the remainder.
- Prime Factors: Prime numbers that multiply together to form the given number.
- Negative Factors: These are negative counterparts of the positive factors.
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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.
