Last updated on August 2nd, 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 schedule events. In this topic, we will learn about the GCF of 14 and 20.
The greatest common factor of 14 and 20 is 2. 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 14 and 20, a few methods are described below -
Steps to find the GCF of 14 and 20 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 14 = 1, 2, 7, 14.
Factors of 20 = 1, 2, 4, 5, 10, 20.
Step 2: Now, identify the common factors of them Common factors of 14 and 20: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 14 and 20 is 2.
To find the GCF of 14 and 20 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 20: 20 = 2 × 2 × 5
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors
The Greatest Common Factor of 14 and 20 is 2.
Find the GCF of 14 and 20 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 20 by 14 20 ÷ 14 = 1 (quotient),
The remainder is calculated as 20 − (14×1) = 6
The remainder is 6, not zero, so continue the process
Step 2: Now divide the previous divisor (14) by the previous remainder (6)
Divide 14 by 6 14 ÷ 6 = 2 (quotient), remainder = 14 − (6×2) = 2
Step 3: Continue the process with the new divisor (6) and remainder (2)
Divide 6 by 2 6 ÷ 2 = 3 (quotient), remainder = 6 − (2×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 14 and 20 is 2.
Finding the GCF of 14 and 20 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A chef has 14 apples and 20 oranges. She wants to arrange them in baskets with the same number of fruits in each basket, using the largest possible number. How many fruits will be in each basket?
We should find the GCF of 14 and 20 GCF of 14 and 20 is 2.
She can have 2 fruits per basket.
As the GCF of 14 and 20 is 2, the chef can arrange the fruits such that each basket contains 2 fruits.
A gardener has 14 rose plants and 20 tulip plants. He wants to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 14 and 20 is 2.
So each row will have 2 plants.
There are 14 rose and 20 tulip plants. To find the total number of plants in each row, we should find the GCF of 14 and 20. There will be 2 plants in each row.
A tailor has 14 meters of red fabric and 20 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 14 and 20.
The GCF of 14 and 20 is 2.
Each piece of fabric will be 2 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 14 and 20, which is 2. The length of each piece of fabric will be 2 meters.
A carpenter has two wooden planks, one 14 cm long and the other 20 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 14 and 20 is 2.
The longest length of each piece is 2 cm.
To find the longest length of each piece of the two wooden planks, 14 cm and 20 cm, respectively, we have to find the GCF of 14 and 20, which is 2 cm. The longest length of each piece is 2 cm.
If the GCF of 14 and ‘b’ is 2, and the LCM is 140. Find ‘b’.
The value of ‘b’ is 20.
GCF × LCM = product of the numbers 2 × 140 = 14 × b
280 = 14b
b = 280 ÷ 14 = 20
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.