100 LearnersLast updated on August 5th, 2025
GCF of 21 and 35
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 to schedule events. In this topic, we will learn about the GCF of 21 and 35.
What is the GCF of 21 and 35?
The greatest common factor of 21 and 35 is 7. 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 35?
To find the GCF of 21 and 35, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 21 and 35 by Using Listing of Factors
Steps to find the GCF of 21 and 35 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 21 = 1, 3, 7, 21.
Factors of 35 = 1, 5, 7, 35.
Step 2: Now, identify the common factors of them Common factors of 21 and 35: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7.
The GCF of 21 and 35 is 7.
GCF of 21 and 35 Using Prime Factorization
To find the GCF of 21 and 35 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 35: 35 = 5 x 7
Step 2: Now, identify the common prime factors
The common prime factor is: 7
Step 3: Multiply the common prime factors
The Greatest Common Factor of 21 and 35 is 7.
GCF of 21 and 35 Using Division Method or Euclidean Algorithm Method
Find the GCF of 21 and 35 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 35 by 21 35 ÷ 21 = 1 (quotient),
The remainder is calculated as 35 − (21×1) = 14
The remainder is 14, not zero, so continue the process
Step 2: Now divide the previous divisor (21) by the previous remainder (14)
Divide 21 by 14 21 ÷ 14 = 1 (quotient), remainder = 21 − (14×1) = 7
The remainder is 7, not zero, so continue the process
Step 3: Now divide the previous divisor (14) by the previous remainder (7)
Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 − (7×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 21 and 35 is 7.
Common Mistakes and How to Avoid Them in GCF of 21 and 35
Finding GCF of 21 and 35 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 the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
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 tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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 an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 21 and 35 Examples
Problem 1
A baker has 21 muffins and 35 cookies. She wants to pack them into boxes with the largest number of items in each box. How many items will be in each box?
We should find the GCF of 21 and 35 GCF of 21 and 35 is 7.
There are 7 equal groups
21 ÷ 7 = 3
35 ÷ 7 = 5
There will be 7 boxes, and each box gets 3 muffins and 5 cookies.
Explanation
As the GCF of 21 and 35 is 7, the baker can make 7 boxes.
Now divide 21 and 35 by 7.
Each box gets 3 muffins and 5 cookies.
Problem 2
A gardener has 21 red flowers and 35 yellow flowers. They want to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?
GCF of 21 and 35 is 7. So each row will have 7 flowers.
Explanation
There are 21 red and 35 yellow flowers.
To find the total number of flowers in each row, we should find the GCF of 21 and 35.
There will be 7 flowers in each row.
Problem 3
A tailor has 21 meters of red ribbon and 35 meters of blue ribbon. She wants to cut both ribbons 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 35 The GCF of 21 and 35 is 7. The ribbon is 7 meters long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 21 and 35, which is 7.
The length of each piece of the ribbon will be 7 meters.
Problem 4
A carpenter has two wooden planks, one 21 cm long and the other 35 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 35 is 7.
The longest length of each piece is 7 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 21 cm and 35 cm, respectively, we have to find the GCF of 21 and 35, which is 7 cm. The longest length of each piece is 7 cm.
Problem 5
If the GCF of 21 and ‘a’ is 7, and the LCM is 105, find ‘a’.
The value of ‘a’ is 35.
Explanation
GCF x LCM = product of the numbers
7 × 105 = 21 × a
735 = 21a
a = 735 ÷ 21 = 35
FAQs on the Greatest Common Factor of 21 and 35
1.What is the LCM of 21 and 35?
2.Is 21 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 35?
5.Are 21 and 35 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 21 and 35?
7.What are some fun ways kids in United Kingdom can practice GCF of 21 and 35 with numbers?
8.What role do numbers and GCF of 21 and 35 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 21 and 35 skills?
Important Glossaries for GCF of 21 and 35
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.
- Prime Factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 35 is 5 x 7.
- Greatest Common Factor (GCF): The largest factor that commonly divides two or more numbers. For example, the GCF of 21 and 35 is 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 21 is divided by 5, the remainder is 1.
- Least Common Multiple (LCM): The smallest common multiple of two or more numbers. For example, the LCM of 21 and 35 is 105.
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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.
