Last updated on August 5th, 2025
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 21 and 15.
The greatest common factor of 21 and 15 is 3. The largest divisor of two or more numbers is called the GCF of the numbers. 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 15, a few methods are described below
Steps to find the GCF of 21 and 15 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 21 = 1, 3, 7, 21.
Factors of 15 = 1, 3, 5, 15.
Step 2: Now, identify the common factors of them Common factors of 21 and 15: 1, 3.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 3.
The GCF of 21 and 15 is 3.
To find the GCF of 21 and 15 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 15: 15 = 3 x 5
Step 2: Now, identify the common prime factors. The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3. The Greatest Common Factor of 21 and 15 is 3.
Find the GCF of 21 and 15 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 21 by 15 21 ÷ 15 = 1 (quotient),
The remainder is calculated as 21 − (15×1) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (15) by the previous remainder (6)
Divide 15 by 6 15 ÷ 6 = 2 (quotient), remainder = 15 − (6×2) = 3
Step 3: Divide the previous divisor (6) by the remainder (3) 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 21 and 15 is 3.
Finding GCF of 21 and 15 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A gardener has 21 tulips and 15 roses. She wants to plant them in equal groups with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 21 and 15 GCF of 21 and 15 3.
There are 3 equal groups
21 ÷ 3 = 7
15 ÷ 3 = 5
There will be 3 groups, and each group gets 7 tulips and 5 roses.
As the GCF of 21 and 15 is 3, the gardener can make 3 groups. Now divide 21 and 15 by 3. Each group gets 7 tulips and 5 roses.
A chef has 21 apples and 15 oranges. He wants to pack them in boxes with the same number of fruits in each box, using the largest possible number of fruits per box. How many fruits will be in each box?
GCF of 21 and 15 3. So each box will have 3 fruits.
There are 21 apples and 15 oranges. To find the total number of fruits in each box, we should find the GCF of 21 and 15. There will be 3 fruits in each box.
A tailor has 21 meters of silk and 15 meters of cotton. 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 15 The GCF of 21 and 15 3. The fabric is 3 meters long.
For calculating the longest length of the fabric, first we need to calculate the GCF of 21 and 15, which is 3. The length of each piece of fabric will be 3 meters.
A carpenter has two wooden planks, one 21 cm long and the other 15 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 15 3. The longest length of each piece is 3 cm.
To find the longest length of each piece of the two wooden planks, 21 cm and 15 cm, respectively.
We have to find the GCF of 21 and 15, which is 3 cm.
The longest length of each piece is 3 cm.
If the GCF of 21 and ‘b’ is 3, and the LCM is 105, find ‘b’.
The value of ‘b’ is 15.
GCF x LCM = product of the numbers
3 × 105 = 21 × b
315 = 21b
b = 315 ÷ 21 = 15
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.