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GCF of 10 and 15

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

1.	GCF of 10 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 15?

Answer: GCF of 10 and 15 is 5.

Explanation:

The GCF of two non-zero integers, x(10) and y(15), is the greatest positive integer m(5) that divides both x(10) and y(15) without any remainder.

Methods to Find GCF of 10 and 15

The methods to find the GCF of 10 and 15 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 10 and 15 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 15: 1, 3, 5, 15

There are 2 common factors of 10 and 15, that are 1 and 5. Therefore, the greatest common factor of 10 and 15 is 5.

GCF of 10 and 15 by Long Division

GCF of 10 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 15 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 10 and 15.

GCF of 10 and 15 by Prime Factorization

Prime factorization of 10 and 15 is (2 × 5) and (3 × 5) respectively. As visible, 10 and 15 have only one common prime factor i.e. 5. Hence, the GCF of 10 and 15 is 5.

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GCF of 10 and 15 Examples

Example 1: Find the greatest number that divides 10 and 15 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 10 × 15
⇒ GCF(10, 15) = (10 × 15)/30 = 5
Therefore, the greatest common factor of 10 and 15 is 5.
Example 3: For two numbers, GCF = 5 and LCM = 30. If one number is 15, find the other number.

Solution:

Given: GCF (z, 15) = 5 and LCM (z, 15) = 30
∵ GCF × LCM = 15 × (z)
⇒ z = (GCF × LCM)/15
⇒ z = (5 × 30)/15
⇒ z = 10
Therefore, the other number is 10.

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FAQs on GCF of 10 and 15

What is the GCF of 10 and 15?

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

How to Find the GCF of 10 and 15 by Long Division Method?

To find the GCF of 10, 15 using long division method, 15 is divided by 10. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 10 and 15?

There are three commonly used methods to find the GCF of 10 and 15.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 10 and 15 by Prime Factorization?

To find the GCF of 10 and 15, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 15 = 3 × 5.
⇒ Since 5 is the only common prime factor of 10 and 15. Hence, GCF (10, 15) = 5.
☛ Prime Number

What is the Relation Between LCM and GCF of 10, 15?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 10 and 15, i.e. GCF × LCM = 10 × 15.

If the GCF of 15 and 10 is 5, Find its LCM.

GCF(15, 10) × LCM(15, 10) = 15 × 10
Since the GCF of 15 and 10 = 5
⇒ 5 × LCM(15, 10) = 150
Therefore, LCM = 30
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