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 3 and 15.
The greatest common factor of 3 and 15 is 3. 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 3 and 15, a few methods are described below -
Steps to find the GCF of 3 and 15 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 3 = 1, 3.
Factors of 15 = 1, 3, 5, 15.
Step 2: Now, identify the common factors of them Common factors of 3 and 15: 1, 3.
Step 3: Choose the largest factor
The largest factor that both numbers have is 3.
The GCF of 3 and 15 is 3.
To find the GCF of 3 and 15 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 3: 3 = 3
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 3 and 15 is 3.
Find the GCF of 3 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 15 by 3 15 ÷ 3 = 5 (quotient),
The remainder is calculated as 15 − (3×5) = 0
The remainder is zero, so the divisor becomes the GCF.
The GCF of 3 and 15 is 3.
Finding GCF of 3 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 teacher has 3 apples and 15 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 the GCF of 3 and 15 GCF of 3 and 15 3
There are 3 equal groups 3 ÷ 3 = 1
15 ÷ 3 = 5
There will be 3 groups, and each group gets 1 apple and 5 oranges.
As the GCF of 3 and 15 is 3, the teacher can make 3 groups. Now divide 3 and 15 by 3. Each group gets 1 apple and 5 oranges.
A school has 3 red flags and 15 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 3 and 15 3
So each row will have 3 flags.
There are 3 red and 15 blue flags. To find the total number of flags in each row, we should find the GCF of 3 and 15. There will be 3 flags in each row.
A tailor has 3 meters of red fabric and 15 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 3 and 15
The GCF of 3 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 3 and 15, which is 3. The length of each piece of the fabric will be 3 meters.
A carpenter has two wooden planks, one 3 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 3 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, 3 cm and 15 cm, respectively. We have to find the GCF of 3 and 15, which is 3 cm. The longest length of each piece is 3 cm.
If the GCF of 3 and ‘a’ is 3, and the LCM is 15, find ‘a’.
The value of ‘a’ is 15.
GCF x LCM = product of the numbers 3 × 15 = 3 × a
45 = 3a
a = 45 ÷ 3 = 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.