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 schedule events. In this topic, we will learn about the GCF of 42 and 56.
The greatest common factor of 42 and 56 is 14. 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 42 and 56, a few methods are described below:
Steps to find the GCF of 42 and 56 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them Common factors of 42 and 56: 1, 2, 7, 14.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 14.
The GCF of 42 and 56 is 14.
To find the GCF of 42 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime factors of 42: 42 = 2 × 3 × 7
Prime factors of 56: 56 = 2 × 2 × 2 × 7 = 2³ × 7
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 × 7
Step 3: Multiply the common prime factors 2 × 7 = 14.
The Greatest Common Factor of 42 and 56 is 14.
Find the GCF of 42 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 56 by 42 56 ÷ 42 = 1 (quotient),
The remainder is calculated as 56 − (42×1) = 14
The remainder is 14, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (14)
Divide 42 by 14 42 ÷ 14 = 3 (quotient), remainder = 42 − (14×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 42 and 56 is 14.
Finding the GCF of 42 and 56 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 42 roses and 56 tulips. She wants to group them into equal sets, with the largest number of items in each group. How many flowers will be in each group?
We should find the GCF of 42 and 56 GCF of 42 and 56
2 × 7 = 14.
There are 14 equal groups
42 ÷ 14 = 3
56 ÷ 14 = 4
There will be 14 groups, and each group gets 3 roses and 4 tulips.
As the GCF of 42 and 56 is 14, the gardener can make 14 groups.
Now divide 42 and 56 by 14.
Each group gets 3 roses and 4 tulips.
A library has 42 English books and 56 French books. They want to arrange them in rows with the same number of books in each row, using the largest possible number of books per row. How many books will be in each row?
GCF of 42 and 56 2 × 7 = 14. So each row will have 14 books.
There are 42 English and 56 French books. To find the total number of books in each row, we should find the GCF of 42 and 56. There will be 14 books in each row.
A tailor has 42 meters of red fabric and 56 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 42 and 56
The GCF of 42 and 56 2 × 7 = 14.
The fabric is 14 meters long.
For calculating the longest length of the fabric, first we need to calculate the GCF of 42 and 56 which is 14. The length of each piece of fabric will be 14 meters.
A carpenter has two wooden planks, one 42 cm long and the other 56 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 42 and 56
2 × 7 = 14.
The longest length of each piece is 14 cm.
To find the longest length of each piece of the two wooden planks, 42 cm and 56 cm, respectively.
We have to find the GCF of 42 and 56, which is 14 cm.
The longest length of each piece is 14 cm.
If the GCF of 42 and ‘b’ is 14, and the LCM is 168. Find ‘b’.
The value of ‘b’ is 56.
GCF × LCM = product of the numbers
14 × 168 = 42 × b
2352 = 42b
b = 2352 ÷ 42 = 56
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.