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

GCF of 30 and 45

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

1.	GCF of 30 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 45?

Answer: GCF of 30 and 45 is 15.

Explanation:

The GCF of two non-zero integers, x(30) and y(45), is the greatest positive integer m(15) that divides both x(30) and y(45) without any remainder.

Methods to Find GCF of 30 and 45

The methods to find the GCF of 30 and 45 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 30 and 45 by Prime Factorization

Prime factorization of 30 and 45 is (2 × 3 × 5) and (3 × 3 × 5) respectively. As visible, 30 and 45 have common prime factors. Hence, the GCF of 30 and 45 is 3 × 5 = 15.

GCF of 30 and 45 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 = 45 and Y = 30

GCF(45, 30) = GCF(30, 45 mod 30) = GCF(30, 15)
GCF(30, 15) = GCF(15, 30 mod 15) = GCF(15, 0)
GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 30 and 45 is 15.

GCF of 30 and 45 by Long Division

GCF of 30 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 30 and 45.

☛ Also Check:

GCF of 30 and 45 Examples

Example 1: Find the greatest number that divides 30 and 45 exactly.

Solution:

The greatest number that divides 30 and 45 exactly is their greatest common factor, i.e. GCF of 30 and 45.
⇒ Factors of 30 and 45:
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 30 and 45 is 15.
Example 2: Find the GCF of 30 and 45, if their LCM is 90.

Solution:

∵ LCM × GCF = 30 × 45
⇒ GCF(30, 45) = (30 × 45)/90 = 15
Therefore, the greatest common factor of 30 and 45 is 15.
Example 3: For two numbers, GCF = 15 and LCM = 90. If one number is 45, find the other number.

Solution:

Given: GCF (z, 45) = 15 and LCM (z, 45) = 90
∵ GCF × LCM = 45 × (z)
⇒ z = (GCF × LCM)/45
⇒ z = (15 × 90)/45
⇒ z = 30
Therefore, the other number is 30.

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 30 and 45

What is the GCF of 30 and 45?

The GCF of 30 and 45 is 15. To calculate the greatest common factor of 30 and 45, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 30 and 45, i.e., 15.

How to Find the GCF of 30 and 45 by Long Division Method?

To find the GCF of 30, 45 using long division method, 45 is divided by 30. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

If the GCF of 45 and 30 is 15, Find its LCM.

GCF(45, 30) × LCM(45, 30) = 45 × 30
Since the GCF of 45 and 30 = 15
⇒ 15 × LCM(45, 30) = 1350
Therefore, LCM = 90
☛ GCF Calculator

What are the Methods to Find GCF of 30 and 45?

There are three commonly used methods to find the GCF of 30 and 45.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and GCF of 30, 45?

The following equation can be used to express the relation between LCM and GCF of 30 and 45, i.e. GCF × LCM = 30 × 45.

How to Find the GCF of 30 and 45 by Prime Factorization?

To find the GCF of 30 and 45, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 45 = 3 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 30 and 45. Hence, GCF(30, 45) = 3 × 5 = 15
☛ What are Prime Numbers?

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum