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 40 and 36.
The greatest common factor of 40 and 36 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 40 and 36, a few methods are described below -
Steps to find the GCF of 40 and 36 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 2: Now, identify the common factors of them Common factors of 40 and 36: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 40 and 36 is 4.
To find the GCF of 40 and 36 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 40: 40 = 2 x 2 x 2 x 5 = 2^3 x 5
Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2^2 x 3^2
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 = 2^2
Step 3: Multiply the common prime factors 2^2 = 4.
The Greatest Common Factor of 40 and 36 is 4.
Find the GCF of 40 and 36 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 40 by 36 40 ÷ 36 = 1 (quotient),
The remainder is calculated as 40 − (36×1) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (36) by the previous remainder (4)
Divide 36 by 4 36 ÷ 4 = 9 (quotient), remainder = 36 − (4×9) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 40 and 36 is 4.
Finding GCF of 40 and 36 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 40 apples and 36 oranges. He wants to distribute them into baskets with the largest number of fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 40 and 36 GCF of 40 and 36 2^2 = 4.
There are 4 equal baskets 40 ÷ 4 = 10
36 ÷ 4 = 9
There will be 4 baskets, and each basket gets 10 apples and 9 oranges.
As the GCF of 40 and 36 is 4, the chef can make 4 baskets. Now divide 40 and 36 by 4. Each basket gets 10 apples and 9 oranges.
A florist has 40 roses and 36 lilies. She wants to create bouquets using the largest number of flowers per bouquet. How many flowers will be in each bouquet?
GCF of 40 and 36 2^2 = 4.
So each bouquet will have 4 flowers.
There are 40 roses and 36 lilies. To find the total number of flowers in each bouquet, we should find the GCF of 40 and 36. There will be 4 flowers in each bouquet.
A tailor has 40 meters of silk and 36 meters of cotton. She wants to cut both materials 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 40 and 36
The GCF of 40 and 36 2^2 = 4.
The material is 4 meters long.
For calculating the longest length of the material, first, we need to calculate the GCF of 40 and 36, which is 4. The length of each piece of the material will be 4 meters.
A carpenter has two wooden planks, one 40 cm long and the other 36 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 40 and 36 2^2 = 4.
The longest length of each piece is 4 cm.
To find the longest length of each piece of the two wooden planks, 40 cm and 36 cm, respectively, we have to find the GCF of 40 and 36, which is 4 cm. The longest length of each piece is 4 cm.
If the GCF of 40 and ‘a’ is 4, and the LCM is 360. Find ‘a’.
The value of ‘a’ is 36.
GCF x LCM = product of the numbers 4 × 360 = 40 × a
1440 = 40a
a = 1440 ÷ 40 = 36
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.