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 to schedule events. In this topic, we will learn about the GCF of 39 and 52.
The greatest common factor of 39 and 52 is 13. 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 52, a few methods are described below
Steps to find the GCF of 39 and 52 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 39 = 1, 3, 13, 39.
Factors of 52 = 1, 2, 4, 13, 26, 52.
Step 2: Now, identify the common factors of them.
Common factors of 39 and 52: 1, 13.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 13.
The GCF of 39 and 52 is 13.
To find the GCF of 39 and 52 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 39: 39 = 3 x 13
Prime Factors of 52: 52 = 2 x 2 x 13 = 2² x 13
Step 2: Now, identify the common prime factors.
The common prime factor is: 13
Step 3: Multiply the common prime factors 13.
The Greatest Common Factor of 39 and 52 is 13.
Find the GCF of 39 and 52 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 52 by 39 52 ÷ 39 = 1 (quotient), The remainder is calculated as 52 − (39×1) = 13
The remainder is 13, not zero, so continue the process
Step 2: Now divide the previous divisor (39) by the previous remainder (13)
Divide 39 by 13 39 ÷ 13 = 3 (quotient), remainder = 39 − (13×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 39 and 52 is 13.
Finding the GCF of 39 and 52 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 39 tulips and 52 roses. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 39 and 52 GCF of 39 and 52 is 13.
There are 13 equal bouquets
39 ÷ 13 = 3
52 ÷ 13 = 4
There will be 13 bouquets, and each bouquet gets 3 tulips and 4 roses.
As the GCF of 39 and 52 is 13, the gardener can make 13 bouquets.
Now divide 39 and 52 by 13.
Each bouquet gets 3 tulips and 4 roses.
A painter has 39 blue cans and 52 red cans. They want to store them in boxes with the same number of cans in each box, using the largest possible number of cans per box. How many cans will be in each box?
GCF of 39 and 52 is 13. So each box will have 13 cans.
There are 39 blue and 52 red cans.
To find the total number of cans in each box, we should find the GCF of 39 and 52.
There will be 13 cans in each box.
A ribbon maker has 39 meters of green ribbon and 52 meters of yellow 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 the longest equal length, we have to calculate the GCF of 39 and 52
The GCF of 39 and 52 is 13.
The ribbon is 13 meters long.
For calculating the longest length of the ribbon, we first need to calculate the GCF of 39 and 52, which is 13.
The length of each piece of the ribbon will be 13 meters.
A carpenter has two wooden planks, one 39 cm long and the other 52 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 52 is 13.
The longest length of each piece is 13 cm.
To find the longest length of each piece of the two wooden planks, 39 cm and 52 cm, respectively. We have to find the GCF of 39 and 52, which is 13 cm.
The longest length of each piece is 13 cm.
If the GCF of 39 and ‘b’ is 13, and the LCM is 156. Find ‘b’.
The value of ‘b’ is 52.
GCF x LCM = product of the numbers
13 × 156 = 39 × b
2028 = 39b
b = 2028 ÷ 39 = 52
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.