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 39 and 6.
The greatest common factor of 39 and 6 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 39 and 6, a few methods are described below -
Steps to find the GCF of 39 and 6 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 39 = 1, 3, 13, 39.
Factors of 6 = 1, 2, 3, 6.
Step 2: Now, identify the common factors of them Common factors of 39 and 6: 1, 3.
Step 3: Choose the largest factor
The largest factor that both numbers have is 3.
The GCF of 39 and 6 is 3.
To find the GCF of 39 and 6 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 39: 39 = 3 × 13
Prime Factors of 6: 6 = 2 × 3
Step 2: Now, identify the common prime factors
The common prime factor is: 3
Step 3: Multiply the common prime factors 3
The Greatest Common Factor of 39 and 6 is 3.
Find the GCF of 39 and 6 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 39 by 6 39 ÷ 6 = 6 (quotient),
The remainder is calculated as 39 − (6×6) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (6) by the previous remainder (3)
Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 39 and 6 is 3.
Finding the GCF of 39 and 6 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A baker has 39 chocolate chips and 6 flour cups. She wants to distribute them into equal sets, with the largest number of items in each set. How many items will be in each set?
We should find the GCF of 39 and 6 GCF of 39 and 6 3
There are 3 equal groups. 39 ÷ 3 = 13 6 ÷ 3 = 2
There will be 3 sets, and each set gets 13 chocolate chips and 2 flour cups.
As the GCF of 39 and 6 is 3, the baker can make 3 sets. Now divide 39 and 6 by 3. Each set gets 13 chocolate chips and 2 flour cups.
A garden has 39 roses and 6 tulips. They want to arrange 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 39 and 6 3
So each row will have 3 flowers.
There are 39 roses and 6 tulips. To find the total number of flowers in each row, we should find the GCF of 39 and 6. There will be 3 flowers in each row.
A tailor has 39 meters of red fabric and 6 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 39 and 6
The GCF of 39 and 6 3
The fabric is 3 meters long.
For calculating the longest length of the fabric, first, we need to calculate the GCF of 39 and 6, which is 3. The length of each piece of fabric will be 3 meters.
A carpenter has two wooden planks, one 39 cm long and the other 6 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 39 and 6 3
The longest length of each piece is 3 cm.
To find the longest length of each piece of the two wooden planks, 39 cm and 6 cm, respectively, we have to find the GCF of 39 and 6, which is 3 cm. The longest length of each piece is 3 cm.
If the GCF of 39 and ‘a’ is 3, and the LCM is 78. Find ‘a’.
The value of ‘a’ is 6.
GCF × LCM = product of the numbers 3 × 78 = 39 × a
234 = 39a
a = 234 ÷ 39 = 6
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.