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 13 and 39.
The greatest common factor of 13 and 39 is 13. 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 13 and 39, a few methods are described below:
Steps to find the GCF of 13 and 39 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 13 = 1, 13.
Factors of 39 = 1, 3, 13, 39.
Step 2: Now, identify the common factors of them.
Common factors of 13 and 39: 1, 13.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 13.
The GCF of 13 and 39 is 13.
To find the GCF of 13 and 39 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 13: 13 is a prime number, so it has only itself as a prime factor.
Prime Factors of 39: 39 = 3 x 13.
Step 2: Now, identify the common prime factors.
The common prime factor is 13.
Step 3: Multiply the common prime factors.
The Greatest Common Factor of 13 and 39 is 13.
Find the GCF of 13 and 39 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 13. 39 ÷ 13 = 3 (quotient), The remainder is calculated as 39 − (13×3) = 0.
The remainder is zero, so the divisor will become the GCF.
The GCF of 13 and 39 is 13.
Finding the GCF of 13 and 39 seems simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A librarian has 13 fiction books and 39 non-fiction books. She wants to arrange them in equal stacks, with each stack having the largest number of books possible. How many books will be in each stack?
We should find the GCF of 13 and 39. GCF of 13 and 39 is 13.
There are 13 equal stacks.
13 ÷ 13 = 1
39 ÷ 13 = 3
There will be 13 stacks, and each stack gets 1 fiction book and 3 non-fiction books.
As the GCF of 13 and 39 is 13, the librarian can make 13 stacks.
Now divide 13 and 39 by 13.
Each stack gets 1 fiction book and 3 non-fiction books.
A farmer has 13 apple trees and 39 orange trees. He wants to plant them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 13 and 39 is 13. So each row will have 13 trees.
There are 13 apple trees and 39 orange trees.
To find the total number of trees in each row, we should find the GCF of 13 and 39.
There will be 13 trees in each row.
A chef has 13 kilograms of flour and 39 kilograms of sugar. She wants to package them in bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 13 and 39.
The GCF of 13 and 39 is 13.
Each bag will weigh 13 kilograms.
For calculating the largest weight for each bag, we first need to calculate the GCF of 13 and 39, which is 13. The weight of each bag will be 13 kilograms.
A decorator has two ribbons, one 13 meters long and the other 39 meters long. She wants to cut them into the longest possible equal pieces, without any ribbon left over. What should be the length of each piece?
The decorator needs the longest piece of ribbon.
GCF of 13 and 39 is 13.
The longest length of each piece is 13 meters.
To find the longest length of each piece of the two ribbons, 13 meters and 39 meters, respectively, we have to find the GCF of 13 and 39, which is 13 meters. The longest length of each piece is 13 meters.
If the GCF of 13 and ‘b’ is 13, and the LCM is 39, find ‘b’.
The value of ‘b’ is 39.
GCF x LCM = product of the numbers
13 × 39 = 13 × b
507 = 13b
b = 507 ÷ 13 = 39
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.