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 48 and 80.
The greatest common factor of 48 and 80 is 16. 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 48 and 80, a few methods are described below:
Steps to find the GCF of 48 and 80 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Step 2: Now, identify the common factors of them.
Common factors of 48 and 80: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 16.
The GCF of 48 and 80 is 16.
To find the GCF of 48 and 80 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 2^4 x 3
Prime Factors of 80: 80 = 2 x 2 x 2 x 2 x 5 = 2^4 x 5
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 48 and 80 is 16.
Find the GCF of 48 and 80 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 80 by 48. 80 ÷ 48 = 1 (quotient),
The remainder is calculated as 80 − (48×1) = 32.
The remainder is 32, not zero, so continue the process.
Step 2: Now divide the previous divisor (48) by the previous remainder (32).
Divide 48 by 32. 48 ÷ 32 = 1 (quotient), remainder = 48 − (32×1) = 16.
The remainder is 16, not zero, so continue the process.
Step 3: Divide the previous divisor (32) by the previous remainder (16). 32 ÷ 16 = 2 (quotient), remainder = 32 − (16×2) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 48 and 80 is 16.
Finding GCF of 48 and 80 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 48 notebooks and 80 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 GCF of 48 and 80
GCF of 48 and 80 is 16.
There are 16 equal groups. 48 ÷ 16 = 3
80 ÷ 16 = 5
There will be 16 groups, and each group gets 3 notebooks and 5 pens.
As the GCF of 48 and 80 is 16, the teacher can make 16 groups. Now divide 48 and 80 by 16. Each group gets 3 notebooks and 5 pens.
A school has 48 red chairs and 80 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 48 and 80 is 16.
So each row will have 16 chairs.
There are 48 red and 80 blue chairs. To find the total number of chairs in each row, we should find the GCF of 48 and 80. There will be 16 chairs in each row.
A tailor has 48 meters of red ribbon and 80 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 48 and 80.
The GCF of 48 and 80 is 16.
The ribbon is 16 meters long.
For calculating the longest length of the ribbon first we need to calculate the GCF of 48 and 80 which is 16. The length of each piece of the ribbon will be 16 meters.
A carpenter has two wooden planks, one 48 cm long and the other 80 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 48 and 80 is 16.
The longest length of each piece is 16 cm.
To find the longest length of each piece of the two wooden planks, 48 cm and 80 cm, respectively. We have to find the GCF of 48 and 80, which is 16 cm. The longest length of each piece is 16 cm.
If the GCF of 48 and ‘a’ is 16, and the LCM is 240. Find ‘a’.
The value of ‘a’ is 80.
GCF x LCM = product of the numbers. 16 × 240 = 48 × a
3840 = 48a
a = 3840 ÷ 48 = 80
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.