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 32 and 56.
The greatest common factor of 32 and 56 is 8. 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 32 and 56, a few methods are described below:
Steps to find the GCF of 32 and 56 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 32 = 1, 2, 4, 8, 16, 32.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them Common factors of 32 and 56: 1, 2, 4, 8.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 8.
The GCF of 32 and 56 is 8.
To find the GCF of 32 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime
Factors of 32: 32 = 2 x 2 x 2 x 2 x 2 = 25
Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 23 x 7
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 2 = 23
Step 3: Multiply the common prime factors 23 = 8.
The Greatest Common Factor of 32 and 56 is 8.
Find the GCF of 32 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 32 56 ÷ 32 = 1 (quotient),
The remainder is calculated as 56 − (32×1) = 24
The remainder is 24, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (24)
Divide 32 by 24 32 ÷ 24 = 1 (quotient), remainder = 32 − (24×1) = 8
Step 3: Continue the process Divide 24 by 8 24 ÷ 8 = 3 (quotient), remainder = 24 − (8×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 32 and 56 is 8.
Finding the GCF of 32 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 teacher has 32 notebooks and 56 pens. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 32 and 56 GCF of 32 and 56
23 = 8.
There are 8 equal groups
32 ÷ 8 = 4
56 ÷ 8 = 7
There will be 8 groups, and each group gets 4 notebooks and 7 pens.
As the GCF of 32 and 56 is 8, the teacher can make 8 groups.
Now divide 32 and 56 by 8.
Each group gets 4 notebooks and 7 pens.
A school has 32 red flags and 56 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 32 and 56 23 = 8. So each row will have 8 flags.
There are 32 red and 56 blue flags.
To find the total number of flags in each row, we should find the GCF of 32 and 56.
There will be 8 flags in each row.
A chef has 32 ounces of flour and 56 ounces of sugar. She wants to divide both into packets of equal weight, using the heaviest possible weight for each packet. What should be the weight of each packet?
For calculating the heaviest equal weight, we have to calculate the GCF of 32 and 56
The GCF of 32 and 56 is 8.
Each packet will weigh 8 ounces.
For calculating the heaviest weight of each packet, first, we need to calculate the GCF of 32 and 56, which is 8. The weight of each packet of flour and sugar will be 8 ounces.
A carpenter has two wooden planks, one 32 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 32 and 56
23 = 8.
The longest length of each piece is 8 cm.
To find the longest length of each piece of the two wooden planks, 32 cm and 56 cm, respectively.
We have to find the GCF of 32 and 56, which is 8 cm.
The longest length of each piece is 8 cm.
If the GCF of 32 and ‘a’ is 8, and the LCM is 224, find ‘a’.
The value of ‘a’ is 56.
GCF x LCM = product of the numbers
8 × 224 = 32 × a
1792 = 32a
a = 1792 ÷ 32 = 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.