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

GCF of 30 and 105

GCF of 30 and 105 is the largest possible number that divides 30 and 105 exactly without any remainder. The factors of 30 and 105 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 3, 5, 7, 15, 21, 35, 105 respectively. There are 3 commonly used methods to find the GCF of 30 and 105 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 30 and 105
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 105?

Answer: GCF of 30 and 105 is 15.

Explanation:

The GCF of two non-zero integers, x(30) and y(105), is the greatest positive integer m(15) that divides both x(30) and y(105) without any remainder.

Methods to Find GCF of 30 and 105

The methods to find the GCF of 30 and 105 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 30 and 105 by Long Division

GCF of 30 and 105 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 105 (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 105.

GCF of 30 and 105 by Prime Factorization

Prime factorization of 30 and 105 is (2 × 3 × 5) and (3 × 5 × 7) respectively. As visible, 30 and 105 have common prime factors. Hence, the GCF of 30 and 105 is 3 × 5 = 15.

GCF of 30 and 105 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105

There are 4 common factors of 30 and 105, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 30 and 105 is 15.

☛ Also Check:

GCF of 30 and 105 Examples

Example 1: Find the greatest number that divides 30 and 105 exactly.

Solution:

The greatest number that divides 30 and 105 exactly is their greatest common factor, i.e. GCF of 30 and 105.
⇒ Factors of 30 and 105:
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105
Therefore, the GCF of 30 and 105 is 15.
Example 2: The product of two numbers is 3150. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 3150
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3150/15
Therefore, the LCM is 210.
Example 3: Find the GCF of 30 and 105, if their LCM is 210.

Solution:

∵ LCM × GCF = 30 × 105
⇒ GCF(30, 105) = (30 × 105)/210 = 15
Therefore, the greatest common factor of 30 and 105 is 15.

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 105

What is the GCF of 30 and 105?

The GCF of 30 and 105 is 15. To calculate the GCF (Greatest Common Factor) of 30 and 105, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105) and choose the greatest factor that exactly divides both 30 and 105, i.e., 15.

If the GCF of 105 and 30 is 15, Find its LCM.

GCF(105, 30) × LCM(105, 30) = 105 × 30
Since the GCF of 105 and 30 = 15
⇒ 15 × LCM(105, 30) = 3150
Therefore, LCM = 210
☛ Greatest Common Factor Calculator

How to Find the GCF of 30 and 105 by Prime Factorization?

To find the GCF of 30 and 105, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 105 = 3 × 5 × 7.
⇒ Since 3, 5 are common terms in the prime factorization of 30 and 105. Hence, GCF(30, 105) = 3 × 5 = 15
☛ Prime Number

What are the Methods to Find GCF of 30 and 105?

There are three commonly used methods to find the GCF of 30 and 105.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 30 and 105 by Long Division Method?

To find the GCF of 30, 105 using long division method, 105 is divided by 30. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 30, 105?

The following equation can be used to express the relation between LCM and GCF of 30 and 105, i.e. GCF × LCM = 30 × 105.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum