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 10 and 24.
The greatest common factor of 10 and 24 is 2. 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 10 and 24, a few methods are described below -
Steps to find the GCF of 10 and 24 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Step 2: Now, identify the common factors of them Common factors of 10 and 24: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 10 and 24 is 2.
To find the GCF of 10 and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 x 5
Prime Factors of 24: 24 = 2 x 2 x 2 x 3
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2.
The Greatest Common Factor of 10 and 24 is 2.
Find the GCF of 10 and 24 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 24 by 10 24 ÷ 10 = 2 (quotient),
The remainder is calculated as 24 − (10×2) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (10) by the previous remainder (4)
Divide 10 by 4 10 ÷ 4 = 2 (quotient), remainder = 10 − (4×2) = 2
Step 3: Repeat the process with the new divisor and remainder
Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 10 and 24 is 2.
Finding GCF of 10 and 24 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 10 loaves of bread and 24 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 the GCF of 10 and 24 GCF of 10 and 24 2.
There are 2 equal groups 10 ÷ 2 = 5
24 ÷ 2 = 12
There will be 2 boxes, and each box gets 5 loaves of bread and 12 muffins.
As the GCF of 10 and 24 is 2, the baker can make 2 boxes. Now divide 10 and 24 by 2. Each box gets 5 loaves of bread and 12 muffins.
A gardener has 10 rose bushes and 24 tulip bulbs. They want to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 10 and 24 2.
So each row will have 2 plants.
There are 10 rose bushes and 24 tulip bulbs. To find the total number of plants in each row, we should find the GCF of 10 and 24. There will be 2 plants in each row.
A tailor has 10 meters of blue fabric and 24 meters of green fabric. 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 10 and 24
The GCF of 10 and 24 2.
The fabric is 2 meters long.
For calculating the longest length of the fabric, first we need to calculate the GCF of 10 and 24, which is 2. The length of each piece of the fabric will be 2 meters.
A carpenter has two wooden planks, one 10 cm long and the other 24 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 10 and 24 2.
The longest length of each piece is 2 cm.
To find the longest length of each piece of the two wooden planks, 10 cm and 24 cm, respectively. We have to find the GCF of 10 and 24, which is 2 cm. The longest length of each piece is 2 cm.
If the GCF of 10 and 'b' is 2, and the LCM is 120. Find 'b'.
The value of ‘b’ is 24.
GCF x LCM = product of the numbers 2 × 120 = 10 × b
240 = 10b
b = 240 ÷ 10 = 24
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.