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 the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 15 and 60.
The greatest common factor of 15 and 60 is 15. 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 15 and 60, a few methods are described below -
Steps to find the GCF of 15 and 60 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 15 = 1, 3, 5, 15.
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Step 2: Now, identify the common factors of them Common factors of 15 and 60: 1, 3, 5, 15.
Step 3: Choose the largest factor
The largest factor that both numbers have is 15.
The GCF of 15 and 60 is 15.
To find the GCF of 15 and 60 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 15: 15 = 3 x 5
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 3 x 5
Step 3: Multiply the common prime factors 3 x 5 = 15.
The Greatest Common Factor of 15 and 60 is 15.
Find the GCF of 15 and 60 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 60 by 15 60 ÷ 15 = 4 (quotient),
The remainder is calculated as 60 − (15×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 15 and 60 is 15.
Finding GCF of 15 and 60 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 15 rose bushes and 60 tulip bulbs. She wants to plant them in equal groups with the largest number of plants in each group. How many plants will be in each group?
We should find GCF of 15 and 60 GCF of 15 and 60 3 x 5 = 15.
There are 15 equal groups 15 ÷ 15 = 1 60 ÷ 15 = 4
There will be 15 groups, and each group gets 1 rose bush and 4 tulip bulbs.
As the GCF of 15 and 60 is 15, the gardener can make 15 groups. Now divide 15 and 60 by 15. Each group gets 1 rose bush and 4 tulip bulbs.
A school has 15 basketballs and 60 soccer balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 15 and 60 3 x 5 = 15.
So each row will have 15 balls.
There are 15 basketballs and 60 soccer balls. To find the total number of balls in each row, we should find the GCF of 15 and 60. There will be 15 balls in each row.
A tailor has 15 meters of silk fabric and 60 meters of cotton 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 15 and 60
The GCF of 15 and 60 3 x 5 = 15.
The fabric is 15 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 15 and 60 which is 15. The length of each piece of fabric will be 15 meters.
A carpenter has two wooden planks, one 15 cm long and the other 60 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 15 and 60 3 x 5 = 15.
The longest length of each piece is 15 cm.
To find the longest length of each piece of the two wooden planks, 15 cm and 60 cm, respectively. We have to find the GCF of 15 and 60, which is 15 cm. The longest length of each piece is 15 cm.
If the GCF of 15 and ‘b’ is 15, and the LCM is 60. Find ‘b’.
The value of ‘b’ is 60.
GCF x LCM = product of the numbers 15 × 60 = 15 × b
900 = 15b
b = 900 ÷ 15 = 60
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.