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 the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 42 and 84.
The greatest common factor of 42 and 84 is 42. 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 42 and 84, a few methods are described below: -
Steps to find the GCF of 42 and 84 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 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Step 2: Now, identify the common factors of them Common factors of 42 and 84: 1, 2, 3, 6, 7, 14, 21, 42.
Step 3: Choose the largest factor
The largest factor that both numbers have is 42.
The GCF of 42 and 84 is 42.
To find the GCF of 42 and 84 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 42: 42 = 2 x 3 x 7
Prime Factors of 84: 84 = 2 x 2 x 3 x 7
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3 x 7
Step 3: Multiply the common prime factors 2 x 3 x 7 = 42.
The Greatest Common Factor of 42 and 84 is 42.
Find the GCF of 42 and 84 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 84 by 42 84 ÷ 42 = 2 (quotient),
The remainder is calculated as 84 − (42×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 42 and 84 is 42.
Finding GCF of 42 and 84 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 apple trees and 84 orange trees. They want to plant the trees in rows, with the largest possible number of trees in each row. How many trees will be in each row?
We should find the GCF of 42 and 84 GCF of 42 and 84 is 42.
There are 42 equal groups. 42 ÷ 42 = 1 84 ÷ 42 = 2
There will be 42 groups, and each group has 1 apple tree and 2 orange trees.
As the GCF of 42 and 84 is 42, the gardener can make 42 groups. Now divide 42 and 84 by 42. Each group has 1 apple tree and 2 orange trees.
A school has 42 red chairs and 84 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 42 and 84 is 42.
So each row will have 42 chairs.
There are 42 red and 84 blue chairs. To find the total number of chairs in each row, we should find the GCF of 42 and 84. There will be 42 chairs in each row.
A chef has 42 meters of red ribbon and 84 meters of blue 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 42 and 84
The GCF of 42 and 84 is 42.
The ribbon is 42 meters long.
For calculating the longest length of the ribbon first we need to calculate the GCF of 42 and 84 which is 42. The length of each piece of the ribbon will be 42 meters.
A carpenter has two wooden planks, one 42 cm long and the other 84 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 84 is 42.
The longest length of each piece is 42 cm.
To find the longest length of each piece of the two wooden planks, 42 cm and 84 cm, respectively. We have to find the GCF of 42 and 84, which is 42 cm. The longest length of each piece is 42 cm.
If the GCF of 42 and ‘a’ is 42, and the LCM is 168, find ‘a’.
The value of ‘a’ is 84.
GCF x LCM = product of the numbers 42 × 168 = 42 × a
7056 = 42a
a = 7056 ÷ 42 = 84
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.