Last updated on August 1st, 2025
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 49.
The greatest common factor of 21 and 49 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.
To find the GCF of 21 and 49, a few methods are described below -
Steps to find the GCF of 21 and 49 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 21 = 1, 3, 7, 21.
Factors of 49 = 1, 7, 49.
Step 2: Now, identify the common factors of them Common factors of 21 and 49: 1, 7.
Step 3: Choose the largest factor
The largest factor that both numbers have is 7.
The GCF of 21 and 49 is 7.
To find the GCF of 21 and 49 using 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 49: 49 = 7 x 7 = 7²
Step 2: Now, identify the common prime factors
The common prime factor is 7.
Step 3: Multiply the common prime factors 7 = 7.
The Greatest Common Factor of 21 and 49 is 7.
Find the GCF of 21 and 49 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 49 by 21 49 ÷ 21 = 2 (quotient),
The remainder is calculated as 49 − (21×2) = 7
The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (21) by the previous remainder (7)
Divide 21 by 7 21 ÷ 7 = 3 (quotient), remainder = 21 − (7×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 21 and 49 is 7.
Finding GCF of 21 and 49 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A teacher has 21 notebooks and 49 pens. 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 49 GCF of 21 and 49 7
There are 7 equal groups 21 ÷ 7 = 3 49 ÷ 7 = 7
There will be 7 groups, and each group gets 3 notebooks and 7 pens.
As the GCF of 21 and 49 is 7, the teacher can make 7 groups. Now divide 21 and 49 by 7. Each group gets 3 notebooks and 7 pens.
A school has 21 red chairs and 49 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 49 7
So each row will have 7 chairs.
There are 21 red and 49 blue chairs. To find the total number of chairs in each row, we should find the GCF of 21 and 49. There will be 7 chairs in each row.
A tailor has 21 meters of red ribbon and 49 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 longest equal length, we have to calculate the GCF of 21 and 49
The GCF of 21 and 49 7
The ribbon is 7 meters long.
For calculating the longest length of the ribbon first we need to calculate the GCF of 21 and 49 which is 7. The length of each piece of the ribbon will be 7 meters.
A gardener has two wooden planks, one 21 cm long and the other 49 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 gardener needs the longest piece of wood GCF of 21 and 49 7
The longest length of each piece is 7 cm.
To find the longest length of each piece of the two wooden planks, 21 cm and 49 cm, respectively. We have to find the GCF of 21 and 49, which is 7 cm. The longest length of each piece is 7 cm.
If the GCF of 21 and ‘a’ is 7, and the LCM is 147. Find ‘a’.
The value of ‘a’ is 49.
GCF x LCM = product of the numbers 7 × 147 = 21 × a
1029 = 21a
a = 1029 ÷ 21 = 49
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.
: She loves to read number jokes and games.