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 12 and 32.
The greatest common factor of 12 and 32 is 4. 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 12 and 32, a few methods are described below -
Steps to find the GCF of 12 and 32 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 12 = 1, 2, 3, 4, 6, 12.
Factors of 32 = 1, 2, 4, 8, 16, 32.
Step 2: Now, identify the common factors of them Common factors of 12 and 32: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 12 and 32 is 4.
To find the GCF of 12 and 32 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3
Prime Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 2⁵
Step 2: Now, identify the common prime factors
The common prime factor is: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4.
The Greatest Common Factor of 12 and 32 is 4.
Find the GCF of 12 and 32 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 32 by 12 32 ÷ 12 = 2 (quotient),
The remainder is calculated as 32 − (12×2) = 8
The remainder is 8, not zero, so continue the process
Step 2: Now divide the previous divisor (12) by the previous remainder (8)
Divide 12 by 8 12 ÷ 8 = 1 (quotient), remainder = 12 − (8×1) = 4
Step 3: Now divide the previous divisor (8) by the previous remainder (4) 8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 12 and 32 is 4.
Finding GCF of 12 and 32 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 12 red flowers and 32 yellow flowers. She wants to arrange them in bouquets with an equal number of flowers, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
We should find the GCF of 12 and 32. GCF of 12 and 32 2² = 4.
There are 4 bouquets. 12 ÷ 4 = 3 32 ÷ 4 = 8
There will be 4 bouquets, and each bouquet gets 3 red flowers and 8 yellow flowers.
As the GCF of 12 and 32 is 4, the gardener can make 4 bouquets. Now divide 12 and 32 by 4. Each bouquet gets 3 red flowers and 8 yellow flowers.
A chef has 12 small plates and 32 large plates. He wants to arrange them in stacks with the same number of plates, using the largest possible number of plates per stack. How many plates will be in each stack?
GCF of 12 and 32 2² = 4.
So each stack will have 4 plates.
There are 12 small plates and 32 large plates. To find the total number of plates in each stack, we should find the GCF of 12 and 32. There will be 4 plates in each stack.
A painter has 12 meters of red paint tape and 32 meters of blue paint tape. He wants to cut both tapes 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 12 and 32.
The GCF of 12 and 32 2² = 4.
The tape is 4 meters long.
For calculating the longest length of the tape, first, we need to calculate the GCF of 12 and 32, which is 4. The length of each piece of the tape will be 4 meters.
A carpenter has two wooden planks, one 12 cm long and the other 32 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 12 and 32 2² = 4.
The longest length of each piece is 4 cm.
To find the longest length of each piece of the two wooden planks, 12 cm and 32 cm, respectively, we have to find the GCF of 12 and 32, which is 4 cm. The longest length of each piece is 4 cm.
If the GCF of 12 and ‘b’ is 4, and the LCM is 96, find ‘b’.
The value of ‘b’ is 32.
GCF x LCM = product of the numbers 4 × 96 = 12 × b
384 = 12b
b = 384 ÷ 12 = 32
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.