A day full of math games & activities. Find one near you.

GCF of 60 and 90

GCF of 60 and 90 is the largest possible number that divides 60 and 90 exactly without any remainder. The factors of 60 and 90 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 60 and 90 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 60 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 60 and 90?

Answer: GCF of 60 and 90 is 30.

Explanation:

The GCF of two non-zero integers, x(60) and y(90), is the greatest positive integer m(30) that divides both x(60) and y(90) without any remainder.

Methods to Find GCF of 60 and 90

Let's look at the different methods for finding the GCF of 60 and 90.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 60 and 90 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 90 and Y = 60

GCF(90, 60) = GCF(60, 90 mod 60) = GCF(60, 30)
GCF(60, 30) = GCF(30, 60 mod 30) = GCF(30, 0)
GCF(30, 0) = 30 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 60 and 90 is 30.

GCF of 60 and 90 by Listing Common Factors

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 8 common factors of 60 and 90, that are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the greatest common factor of 60 and 90 is 30.

GCF of 60 and 90 by Long Division

GCF of 60 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 60 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (60) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (30) is the GCF of 60 and 90.

☛ Also Check:

GCF of 60 and 90 Examples

Example 1: Find the GCF of 60 and 90, if their LCM is 180.

Solution:

∵ LCM × GCF = 60 × 90
⇒ GCF(60, 90) = (60 × 90)/180 = 30
Therefore, the greatest common factor of 60 and 90 is 30.
Example 2: Find the greatest number that divides 60 and 90 exactly.

Solution:

The greatest number that divides 60 and 90 exactly is their greatest common factor, i.e. GCF of 60 and 90.
⇒ Factors of 60 and 90:
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the GCF of 60 and 90 is 30.
Example 3: The product of two numbers is 5400. If their GCF is 30, what is their LCM?

Solution:

Given: GCF = 30 and product of numbers = 5400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5400/30
Therefore, the LCM is 180.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 60 and 90

What is the GCF of 60 and 90?

The GCF of 60 and 90 is 30. To calculate the GCF (Greatest Common Factor) of 60 and 90, we need to factor each number (factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 60 and 90, i.e., 30.

If the GCF of 90 and 60 is 30, Find its LCM.

GCF(90, 60) × LCM(90, 60) = 90 × 60
Since the GCF of 90 and 60 = 30
⇒ 30 × LCM(90, 60) = 5400
Therefore, LCM = 180
☛ Greatest Common Factor Calculator

How to Find the GCF of 60 and 90 by Long Division Method?

To find the GCF of 60, 90 using long division method, 90 is divided by 60. The corresponding divisor (30) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 60 and 90?

There are three commonly used methods to find the GCF of 60 and 90.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 60, 90?

The following equation can be used to express the relation between Least Common Multiple and GCF of 60 and 90, i.e. GCF × LCM = 60 × 90.

How to Find the GCF of 60 and 90 by Prime Factorization?

To find the GCF of 60 and 90, we will find the prime factorization of the given numbers, i.e. 60 = 2 × 2 × 3 × 5; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3, 5 are common terms in the prime factorization of 60 and 90. Hence, GCF(60, 90) = 2 × 3 × 5 = 30
☛ What are Prime Numbers?

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum