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 96.
The greatest common factor of 42 and 96 is 6. 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 96, a few methods are described below -
Steps to find the GCF of 42 and 96 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 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
Step 2: Now, identify the common factors of them
Common factors of 42 and 96: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 42 and 96 is 6.
To find the GCF of 42 and 96 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 96: 96 = 2 x 2 x 2 x 2 x 2 x 3 = 25 x 3
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3
Step 3: Multiply the common prime factors 2 x 3 = 6.
The Greatest Common Factor of 42 and 96 is 6.
Find the GCF of 42 and 96 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 96 by 42 96 ÷ 42 = 2 (quotient),
The remainder is calculated as 96 − (42×2) = 12
The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (42) by the previous remainder (12)
Divide 42 by 12 42 ÷ 12 = 3 (quotient), remainder = 42 − (12×3) = 6
The remainder is not zero, so continue the process
Step 3: Divide the previous divisor (12) by the previous remainder (6) 12 ÷ 6 = 2 (quotient), remainder = 12 − (6×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 42 and 96 is 6.
Finding GCF of 42 and 96 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 rose bushes and 96 tulip bulbs. He wants to divide them into the largest equal groups possible. How many plants will be in each group?
We should find GCF of 42 and 96 The GCF of 42 and 96 is 6. 42 ÷ 6 = 7 96 ÷ 6 = 16 There will be 6 groups, and each group will contain 7 rose bushes and 16 tulip bulbs.
As the GCF of 42 and 96 is 6, the gardener can make 6 groups.
Now divide 42 and 96 by 6.
Each group will have 7 rose bushes and 16 tulip bulbs.
A mechanic has 42 wrenches and 96 screwdrivers. He wants to organize them into toolkits with the greatest number of each tool in every kit. How many tools will each toolkit have?
The GCF of 42 and 96 is 6. So each toolkit will have 6 tools.
There are 42 wrenches and 96 screwdrivers.
To find the total number of tools in each toolkit, we should find the GCF of 42 and 96.
There will be 6 tools in each toolkit.
A chef has 42 kg of potatoes and 96 kg of onions. She wants to pack them into bags with the largest possible weight each. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 42 and 96. The GCF of 42 and 96 is 6. Each bag will weigh 6 kg.
For calculating the largest weight of the bags, first we need to calculate the GCF of 42 and 96, which is 6.
The weight of each bag will be 6 kg.
A tailor has two bolts of fabric, one 42 meters long and the other 96 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric. The GCF of 42 and 96 is 6. The longest length of each piece is 6 meters.
To find the longest length of each piece of the two bolts of fabric, 42 meters and 96 meters, respectively.
have to find the GCF of 42 and 96, which is 6 meters.
The longest length of each piece is 6 meters.
If the GCF of 42 and ‘b’ is 6, and the LCM is 672. Find ‘b’.
The value of ‘b’ is 96.
GCF x LCM = product of the numbers
6 × 672 = 42 × b
4032 = 42b
b = 4032 ÷ 42 = 96
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.