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 4 and 10.
The greatest common factor of 4 and 10 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 4 and 10, a few methods are described below -
Steps to find the GCF of 4 and 10 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 4 = 1, 2, 4.
Factors of 10 = 1, 2, 5, 10.
Step 2: Now, identify the common factors of them Common factors of 4 and 10: 1, 2.
Step 3: Choose the largest factor
The largest factor that both numbers have is 2.
The GCF of 4 and 10 is 2.
To find the GCF of 4 and 10 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime factors of 4: 4 = 2 x 2 = 2²
Prime factors of 10: 10 = 2 x 5
Step 2: Now, identify the common prime factors
The common prime factor is: 2
Step 3: Multiply the common prime factors
The Greatest Common Factor of 4 and 10 is 2.
Find the GCF of 4 and 10 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 10 by 4 10 ÷ 4 = 2 (quotient),
The remainder is calculated as 10 − (4×2) = 2
The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (4) by the previous remainder (2)
Divide 4 by 2 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 4 and 10 is 2.
Finding the GCF of 4 and 10 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A chef has 4 apples and 10 oranges. He wants to arrange them in equal baskets with the largest number of items in each basket. How many items will be in each basket?
We should find the GCF of 4 and 10 GCF of 4 and 10 is 2.
There are 2 equal baskets 4 ÷ 2 = 2 10 ÷ 2 = 5
There will be 2 baskets, and each basket gets 2 apples and 5 oranges.
As the GCF of 4 and 10 is 2, the chef can make 2 baskets. Now divide 4 and 10 by 2. Each basket gets 2 apples and 5 oranges.
A school has 4 red flags and 10 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 4 and 10 is 2.
So each row will have 2 flags.
There are 4 red flags and 10 blue flags. To find the total number of flags in each row, we should find the GCF of 4 and 10. There will be 2 flags in each row.
A gardener has 4 meters of green tape and 10 meters of blue tape. She wants to cut both tapes 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 4 and 10
The GCF of 4 and 10 is 2.
The tape pieces are 2 meters long.
For calculating the longest length of the tape, first we need to calculate the GCF of 4 and 10, which is 2. The length of each piece of tape will be 2 meters.
A carpenter has two wooden planks, one 4 cm long and the other 10 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 4 and 10 is 2.
The longest length of each piece is 2 cm.
To find the longest length of each piece of the two wooden planks, 4 cm and 10 cm, respectively, we have to find the GCF of 4 and 10, which is 2 cm. The longest length of each piece is 2 cm.
If the GCF of 4 and ‘b’ is 2, and the LCM is 20. Find ‘b’.
The value of ‘b’ is 10.
GCF x LCM = product of the numbers 2 × 20 = 4 × b
40 = 4b
b = 40 ÷ 4 = 10
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.