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104 LearnersLast updated on September 25, 2025
GCF of 66 and 90
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 66 and 90.
What is the GCF of 66 and 90?
The greatest common factor of 66 and 90 is 6. 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.
How to find the GCF of 66 and 90?
To find the GCF of 66 and 90, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 66 and 90 by Using Listing of Factors
Steps to find the GCF of 66 and 90 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66. 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 66 and 90: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6. The GCF of 66 and 90 is 6.
GCF of 66 and 90 Using Prime Factorization
To find the GCF of 66 and 90 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 66: 66 = 2 × 3 × 11 Prime Factors of 90: 90 = 2 × 3 × 3 × 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 3
Step 3: Multiply the common prime factors 2 × 3 = 6. The Greatest Common Factor of 66 and 90 is 6.
GCF of 66 and 90 Using Division Method or Euclidean Algorithm Method
Find the GCF of 66 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 66 90 ÷ 66 = 1 (quotient), The remainder is calculated as 90 − (66×1) = 24 The remainder is 24, not zero, so continue the process
Step 2: Now divide the previous divisor (66) by the previous remainder (24) Divide 66 by 24 66 ÷ 24 = 2 (quotient), remainder = 66 − (24×2) = 18 The remainder is 18, not zero, so continue the process
Step 3: Now divide the previous divisor (24) by the previous remainder (18) Divide 24 by 18 24 ÷ 18 = 1 (quotient), remainder = 24 − (18×1) = 6 The remainder is 6, not zero, so continue the process
Step 4: Now divide the previous divisor (18) by the previous remainder (6) Divide 18 by 6 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 66 and 90 is 6.
Common Mistakes and How to Avoid Them in GCF of 66 and 90
Finding the GCF of 66 and 90 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 66, students may mention 8, which is incorrect.
To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 66 and 90 Examples
Problem 1
A florist has 66 roses and 90 tulips. She wants to create bouquets with the same number of flowers in each, using the largest number of flowers possible. How many flowers will be in each bouquet?
We should find the GCF of 66 and 90 GCF of 66 and 90 2 × 3 = 6. There are 6 equal bouquets 66 ÷ 6 = 11 90 ÷ 6 = 15 There will be 6 bouquets, and each bouquet gets 11 roses and 15 tulips.
Explanation
As the GCF of 66 and 90 is 6, the florist can make 6 bouquets.
Now divide 66 and 90 by 6.
Each bouquet gets 11 roses and 15 tulips.
Problem 2
A chef has 66 chocolate bars and 90 marshmallows. He wants to create dessert plates with the same number of treats on each plate, using the largest number of treats possible. How many treats will be on each plate?
GCF of 66 and 90 2 × 3 = 6. So each plate will have 6 treats.
Explanation
There are 66 chocolate bars and 90 marshmallows.
To find the total number of treats in each plate, we should find the GCF of 66 and 90.
There will be 6 treats on each plate.
Problem 3
A seamstress has 66 meters of silk fabric and 90 meters of cotton 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 66 and 90 The GCF of 66 and 90 2 × 3 = 6. The fabric pieces are 6 meters long.
Explanation
To calculate the longest length of the fabric, first, we need to calculate the GCF of 66 and 90, which is 6.
The length of each piece of fabric will be 6 meters.
Problem 4
A carpenter has two wooden planks, one 66 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 66 and 90 2 × 3 = 6. The longest length of each piece is 6 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 66 cm and 90 cm, respectively, we have to find the GCF of 66 and 90, which is 6 cm.
The longest length of each piece is 6 cm.
Problem 5
If the GCF of 66 and ‘b’ is 6, and the LCM is 990, find ‘b’.
The value of ‘b’ is 90.
Explanation
GCF × LCM = product of the numbers
6 × 990 = 66 × b
5940 = 66b
b = 5940 ÷ 66
= 90
FAQs on the Greatest Common Factor of 66 and 90
1.What is the LCM of 66 and 90?
2.Is 66 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 90?
5.Are 66 and 90 prime numbers?
Important Glossaries for GCF of 66 and 90
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
