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 32 and 48.
The greatest common factor of 32 and 48 is 16. 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 48, a few methods are described below
Steps to find the GCF of 32 and 48 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 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Step 2: Now, identify the common factors of them Common factors of 32 and 48: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor
The largest factor that both numbers have is 16.
The GCF of 32 and 48 is 16.
To find the GCF of 32 and 48 using 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 = 2^5
Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2^4 x 3
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 2 x 2 = 2^4
Step 3: Multiply the common prime factors 2^4 = 16.
The Greatest Common Factor of 32 and 48 is 16.
Find the GCF of 32 and 48 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 48 by 32 48 ÷ 32 = 1 (quotient),
The remainder is calculated as 48 − (32×1) = 16
The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (32) by the previous remainder (16)
Divide 32 by 16 32 ÷ 16 = 2 (quotient), remainder = 32 − (16×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 32 and 48 is 16.
Finding GCF of 32 and 48 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A baker has 32 loaves of bread and 48 muffins. She wants to pack them into boxes with the largest number of items in each box. How many items will be in each box?
We should find GCF of 32 and 48 GCF of 32 and 48 2^4 = 16.
There are 16 items in each box. 32 ÷ 16 = 2 48 ÷ 16 = 3
There will be 16 boxes, and each box gets 2 loaves of bread and 3 muffins.
As the GCF of 32 and 48 is 16, the baker can make 16 boxes.
Now divide 32 and 48 by 16.
Each box gets 2 loaves of bread and 3 muffins.
A school has 32 tables and 48 chairs. They want to arrange them in rows with the same number of pieces of furniture in each row, using the largest possible number of pieces per row. How many pieces will be in each row?
GCF of 32 and 48 2^4 = 16. So each row will have 16 pieces.
There are 32 tables and 48 chairs.
To find the total number of pieces of furniture in each row, we should find the GCF of 32 and 48.
There will be 16 pieces in each row.
A gardener has 32 meters of hose and 48 meters of cable. She wants to cut both into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 32 and 48
The GCF of 32 and 48 2^4 = 16.
The pieces will be 16 meters long.
For calculating the longest length of the hose and cable, first, we need to calculate the GCF of 32 and 48, which is 16.
The length of each piece will be 16 meters.
A carpenter has two wooden planks, one 32 cm long and the other 48 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 48 2^4 = 16.
The longest length of each piece is 16 cm.
To find the longest length of each piece of the two wooden planks, 32 cm and 48 cm, respectively, we have to find the GCF of 32 and 48, which is 16 cm.
The longest length of each piece is 16 cm.
If the GCF of 32 and ‘a’ is 16, and the LCM is 96, find ‘a’.
The value of ‘a’ is 48.
GCF x LCM = product of the numbers 16 × 96 = 32 × a
1536 = 32a
a = 1536 ÷ 32 = 48
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.