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 24 and 90.
The greatest common factor of 24 and 90 is 6. 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 24 and 90, a few methods are described below -
Steps to find the GCF of 24 and 90 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 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Step 2: Now, identify the common factors of them Common factors of 24 and 90: 1, 2, 3, 6.
Step 3: Choose the largest factor
The largest factor that both numbers have is 6.
The GCF of 24 and 90 is 6.
To find the GCF of 24 and 90 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2³ x 3
Prime Factors of 90: 90 = 2 x 3 x 3 x 5 = 2 x 3² x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 3 = 2¹ x 3¹
Step 3: Multiply the common prime factors 2¹ x 3¹ = 2 x 3 = 6.
The Greatest Common Factor of 24 and 90 is 6.
Find the GCF of 24 and 90 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 90 by 24 90 ÷ 24 = 3 (quotient),
The remainder is calculated as 90 − (24×3) = 18
The remainder is 18, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (18)
Divide 24 by 18 24 ÷ 18 = 1 (quotient), remainder = 24 − (18×1) = 6
Step 3: Continue the process. Now divide the previous divisor (18) by the previous remainder (6) 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0
The remainder is zero, so the divisor at this step is the GCF.
The GCF of 24 and 90 is 6.
Finding GCF of 24 and 90 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A florist has 24 roses and 90 tulips. She wants to create bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find GCF of 24 and 90 GCF of 24 and 90 2 x 3 = 6.
There are 6 flowers in each bouquet. 24 ÷ 6 = 4
90 ÷ 6 = 15
There will be 6 bouquets, and each bouquet gets 4 roses and 15 tulips.
As the GCF of 24 and 90 is 6, the florist can make bouquets with 6 flowers each. Now divide 24 and 90 by 6. Each bouquet gets 4 roses and 15 tulips.
A farmer has 24 apple trees and 90 orange trees. He wants to arrange them in rows with the same number of trees in each row, using the largest possible number of trees per row. How many trees will be in each row?
GCF of 24 and 90 2 x 3 = 6.
So each row will have 6 trees.
There are 24 apple trees and 90 orange trees. To find the total number of trees in each row, we should find the GCF of 24 and 90. There will be 6 trees in each row.
A chef has 24 kg of flour and 90 kg of sugar. She wants to package them into bags of equal weight, using the largest possible weight for each bag. What should be the weight of each bag?
For calculating the largest equal weight, we have to calculate the GCF of 24 and 90
The GCF of 24 and 90
2 x 3 = 6.
Each bag will weigh 6 kg.
For calculating the largest weight of each bag, first we need to calculate the GCF of 24 and 90 which is 6. The weight of each bag will be 6 kg.
A gardener has two pieces of land, one 24 meters wide and the other 90 meters wide. He wants to divide them into the longest possible equal sections. What should be the width of each section?
The gardener needs the longest section width GCF of 24 and 90 2 x 3 = 6.
The longest width of each section is 6 meters.
To find the longest width of each section of the two pieces of land, 24 meters and 90 meters wide respectively. We have to find the GCF of 24 and 90, which is 6 meters. The longest width of each section is 6 meters.
If the GCF of 24 and ‘b’ is 6, and the LCM is 360. Find ‘b’.
The value of ‘b’ is 90.
GCF x LCM = product of the numbers 6 x 360 = 24 x b
2160 = 24b
b = 2160 ÷ 24 = 90
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.