Last updated on August 5th, 2025
The GCF, or greatest common factor, is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 14 and 49.
The greatest common factor of 14 and 49 is 7. The largest divisor of two or more numbers is called the GCF of those 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 14 and 49, a few methods are described below:
Steps to find the GCF of 14 and 49 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 14 = 1, 2, 7, 14.
Factors of 49 = 1, 7, 49.
Step 2: Now, identify the common factors of them. Common factors of 14 and 49: 1, 7.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 7.
The GCF of 14 and 49 is 7.
To find the GCF of 14 and 49 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 14: 14 = 2 × 7
Prime Factors of 49: 49 = 7 × 7
Step 2: Now, identify the common prime factors.
The common prime factor is 7.
Step 3: Multiply the common prime factors.
The Greatest Common Factor of 14 and 49 is 7.
Find the GCF of 14 and 49 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 49 by 14. 49 ÷ 14 = 3 (quotient), The remainder is calculated as 49 − (14×3) = 7.
The remainder is 7, not zero, so continue the process.
Step 2: Now divide the previous divisor (14) by the previous remainder (7).
Divide 14 by 7. 14 ÷ 7 = 2 (quotient), remainder = 14 − (7×2) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 14 and 49 is 7.
Finding the GCF of 14 and 49 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 14 loaves of white bread and 49 loaves of whole wheat bread. She wants to package them into equal sets, with the largest number of loaves in each set. How many loaves will be in each set?
We should find the GCF of 14 and 49.
The GCF of 14 and 49 is 7.
There are 7 equal groups.
14 ÷ 7 = 2
49 ÷ 7 = 7
There will be 7 groups, and each group gets 2 loaves of white bread and 7 loaves of whole wheat bread.
As the GCF of 14 and 49 is 7, the baker can make 7 groups.
Now divide 14 and 49 by 7.
Each group gets 2 loaves of white bread and 7 loaves of whole wheat bread.
A park has 14 oak trees and 49 maple trees. They want 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?
The GCF of 14 and 49 is 7. So each row will have 7 trees.
There are 14 oak and 49 maple trees.
To find the total number of trees in each row, we should find the GCF of 14 and 49.
There will be 7 trees in each row.
A tailor has 14 meters of silk fabric and 49 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 14 and 49.
The GCF of 14 and 49 is 7.
The fabric is cut into pieces of 7 meters long.
For calculating the longest length of the fabric first, we need to calculate the GCF of 14 and 49, which is 7. The length of each piece of the fabric will be 7 meters.
A carpenter has two wooden planks, one 14 cm long and the other 49 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.
The GCF of 14 and 49 is 7.
The longest length of each piece is 7 cm.
To find the longest length of each piece of the two wooden planks, 14 cm and 49 cm, respectively, we have to find the GCF of 14 and 49, which is 7 cm. The longest length of each piece is 7 cm.
If the GCF of 14 and ‘b’ is 7, and the LCM is 98, find ‘b’.
The value of ‘b’ is 49.
GCF × LCM = product of the numbers
7 × 98 = 14 × b
686 = 14b
b = 686 ÷ 14 = 49
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.