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 72 and 90.
The greatest common factor of 72 and 90 is 18. 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 72 and 90, a few methods are described below:
Steps to find the GCF of 72 and 90 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
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 72 and 90: 1, 2, 3, 6, 9, 18.
Step 3: Choose the largest factor. The largest factor that both numbers have is 18. The GCF of 72 and 90 is 18.
To find the GCF of 72 and 90 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32
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 x 3 = 2 x 32
Step 3: Multiply the common prime factors 2 x 32 = 2 x 9 = 18.
The Greatest Common Factor of 72 and 90 is 18.
Find the GCF of 72 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 72 90 ÷ 72 = 1 (quotient), The remainder is calculated as 90 − (72×1) = 18
The remainder is 18, not zero, so continue the process
Step 2: Now divide the previous divisor (72) by the previous remainder (18)
Divide 72 by 18 72 ÷ 18 = 4 (quotient), remainder = 72 − (18×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 72 and 90 is 18.
Finding GCF of 72 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 baker has 72 chocolate muffins and 90 vanilla muffins. He wants to pack them into boxes with the largest number of muffins in each box, ensuring each box has the same number of muffins. How many muffins will be in each box?
We should find the GCF of 72 and 90 GCF of 72 and 90
2 x 32 = 2 x 9 = 18.
There are 18 muffins in each box
72 ÷ 18 = 4
90 ÷ 18 = 5
There will be 18 muffins per box, and each box will contain 4 chocolate muffins and 5 vanilla muffins.
As the GCF of 72 and 90 is 18, the baker can make 18 muffins per box.
Now divide 72 and 90 by 18.
Each box will contain 4 chocolate muffins and 5 vanilla muffins.
A gardener has 72 tulips and 90 roses. She wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?
GCF of 72 and 90
2 x 32 = 2 x 9 = 18.
So each row will have 18 flowers.
There are 72 tulips and 90 roses.
To find the total number of flowers in each row, we should find the GCF of 72 and 90.
There will be 18 flowers in each row.
A tailor has 72 meters of silk and 90 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 72 and 90.
The GCF of 72 and 90 2 x 32 = 2 x 9 = 18.
The fabric is 18 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 72 and 90 which is 18.
The length of each piece of fabric will be 18 meters.
A carpenter has two wooden planks, one 72 cm long and the other 90 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 72 and 90
2 x 32 = 2 x 9 = 18.
The longest length of each piece is 18 cm.
To find the longest length of each piece of the two wooden planks, 72 cm and 90 cm, respectively.
We have to find the GCF of 72 and 90, which is 18 cm.
The longest length of each piece is 18 cm.
If the GCF of 72 and ‘a’ is 18, and the LCM is 360. Find ‘a’.
The value of ‘a’ is 90.
GCF x LCM = product of the numbers
18 × 360 = 72 × a
6480 = 72a
a = 6480 ÷ 72 = 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.