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Last updated on August 14, 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, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 24 and 52.
The greatest common factor of 24 and 52 is 4. 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 24 and 52, a few methods are described below -
Steps to find the GCF of 24 and 52 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24. Factors of 52 = 1, 2, 4, 13, 26, 52.
Step 2: Now, identify the common factors of them Common factors of 24 and 52: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 24 and 52 is 4.
To find the GCF of 24 and 52 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3
Prime Factors of 52: 52 = 2 × 2 × 13 = 2² × 13
Step 2: Now, identify the common prime factors The common prime factor is: 2 × 2 = 2²
Step 3: Multiply the common prime factors 2² = 4 The Greatest Common Factor of 24 and 52 is 4.
Find the GCF of 24 and 52 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 52 by 24 52 ÷ 24 = 2 (quotient), The remainder is calculated as 52 − (24×2) = 4 The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (4) Divide 24 by 4 24 ÷ 4 = 6 (quotient), remainder = 0 The remainder is zero, so the divisor will become the GCF. The GCF of 24 and 52 is 4.
Finding GCF of 24 and 52 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 24 notebooks and 52 markers. 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 24 and 52. GCF of 24 and 52 is 4.
There are 4 equal groups. 24 ÷ 4 = 6 52 ÷ 4 = 13
There will be 4 groups, and each group gets 6 notebooks and 13 markers.
As the GCF of 24 and 52 is 4, the teacher can make 4 groups. Now divide 24 and 52 by 4. Each group gets 6 notebooks and 13 markers.
A school has 24 green desks and 52 yellow desks. They want to arrange them in rows with the same number of desks in each row, using the largest possible number of desks per row. How many desks will be in each row?
GCF of 24 and 52 is 4. So each row will have 4 desks.
There are 24 green and 52 yellow desks. To find the total number of desks in each row, we should find the GCF of 24 and 52. There will be 4 desks in each row.
A tailor has 24 meters of silk and 52 meters of cotton. She wants to cut both fabrics 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 24 and 52. The GCF of 24 and 52 is 4. The length of each piece is 4 meters.
For calculating the longest length of the fabric pieces, we first need to calculate the GCF of 24 and 52, which is 4. The length of each piece of fabric will be 4 meters.
A carpenter has two wooden planks, one 24 cm long and the other 52 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 24 and 52 is 4. The longest length of each piece is 4 cm.
To find the longest length of each piece of the two wooden planks, 24 cm and 52 cm, respectively, we have to find the GCF of 24 and 52, which is 4 cm. The longest length of each piece is 4 cm.
If the GCF of 24 and ‘a’ is 4, and the LCM is 312, find ‘a’.
The value of ‘a’ is 52.
GCF × LCM = product of the numbers
4 × 312 = 24 × a
1,248 = 24a
a = 1,248 ÷ 24 = 52
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.