102 LearnersLast updated on August 12th, 2025
GCF of 21 and 40
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 21 and 40.
What is the GCF of 21 and 40?
The greatest common factor of 21 and 40 is 1. The largest divisor of two or more numbers is called the GCF of the number.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 21 and 40?
To find the GCF of 21 and 40, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 21 and 40 by Using Listing of factors
Steps to find the GCF of 21 and 40 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 21 = 1, 3, 7, 21. Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40.
Step 2: Now, identify the common factors of them Common factors of 21 and 40: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 21 and 40 is 1.
GCF of 21 and 40 Using Prime Factorization
To find the GCF of 21 and 40 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number Prime Factors of 21: 21 = 3 x 7 Prime Factors of 40: 40 = 2 x 2 x 2 x 5 = 2³ x 5
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
GCF of 21 and 40 Using Division Method or Euclidean Algorithm Method
Find the GCF of 21 and 40 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 40 by 21 40 ÷ 21 = 1 (quotient), The remainder is calculated as 40 − (21×1) = 19 The remainder is 19, not zero, so continue the process
Step 2: Now divide the previous divisor (21) by the previous remainder (19) Divide 21 by 19 21 ÷ 19 = 1 (quotient), remainder = 21 − (19×1) = 2 The remainder is 2, not zero, so continue the process
Step 3: Now divide the previous divisor (19) by the previous remainder (2) 19 ÷ 2 = 9 (quotient), remainder = 19 − (2×9) = 1 The remainder is 1, not zero, so continue the process
Step 4: Now divide the previous divisor (2) by the previous remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0 The remainder is zero, so the divisor will become the GCF. The GCF of 21 and 40 is 1.
Common Mistakes and How to Avoid Them in GCF of 21 and 40
Finding GCF of 21 and 40 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 21, students may mention 10 which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select a factor other than 1 as a common factor. To avoid this confusion, students should list all the common factors and correctly identify that 1 is the only common factor.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But it's not true; the GCF can be 1, especially when the numbers are co-prime. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 21 and 40 Examples
Problem 1
A teacher has 21 apples and 40 oranges. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find GCF of 21 and 40 GCF of 21 and 40 is 1. There are 1 equal group. 21 ÷ 1 = 21 40 ÷ 1 = 40
There will be 1 group, and each group gets all the apples and oranges.
Explanation
As the GCF of 21 and 40 is 1, the teacher can make only 1 group. Now divide 21 and 40 by 1. Each group gets all the apples and oranges.
Problem 2
A school has 21 red chairs and 40 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 21 and 40 is 1. So each row will have 1 chair.
Explanation
There are 21 red and 40 blue chairs. To find the total number of chairs in each row, we should find the GCF of 21 and 40. There will be 1 chair in each row.
Problem 3
A tailor has 21 meters of red fabric and 40 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 21 and 40 The GCF of 21 and 40 is 1. The fabric is 1 meter long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 21 and 40, which is 1. The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 21 cm long and the other 40 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 21 and 40 is 1. The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 21 cm and 40 cm, respectively, we have to find the GCF of 21 and 40, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 21 and ‘a’ is 1, and the LCM is 420. Find ‘a’.
The value of ‘a’ is 20.
Explanation
GCF x LCM = product of the numbers
1 × 420 = 21 × a
420 = 21a
a = 420 ÷ 21 = 20
FAQs on the Greatest Common Factor of 21 and 40
1.What is the LCM of 21 and 40?
2.Is 21 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 21?
5.Are 21 and 40 prime numbers?
6.How can children in Australia use numbers in everyday life to understand GCF of 21 and 40?
7.What are some fun ways kids in Australia can practice GCF of 21 and 40 with numbers?
8.What role do numbers and GCF of 21 and 40 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve GCF of 21 and 40 skills?
Important Glossaries for GCF of 21 and 40
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.
- Prime Numbers: Numbers that have only two distinct positive divisors, 1 and the number itself. For example, 3 and 7 are primes.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 21 are 3 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 40 is divided by 21, the remainder is 19.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 21 and 40 is 840.
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.
