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GCF of 15 and 21

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

1.	GCF of 15 and 21
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 21?

Answer: GCF of 15 and 21 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(21), is the greatest positive integer m(3) that divides both x(15) and y(21) without any remainder.

Methods to Find GCF of 15 and 21

The methods to find the GCF of 15 and 21 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 15 and 21 by Long Division

GCF of 15 and 21 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 21 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 21.

GCF of 15 and 21 by Prime Factorization

Prime factorization of 15 and 21 is (3 × 5) and (3 × 7) respectively. As visible, 15 and 21 have only one common prime factor i.e. 3. Hence, the GCF of 15 and 21 is 3.

GCF of 15 and 21 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 21: 1, 3, 7, 21

There are 2 common factors of 15 and 21, that are 1 and 3. Therefore, the greatest common factor of 15 and 21 is 3.

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GCF of 15 and 21 Examples

Example 1: Find the GCF of 15 and 21, if their LCM is 105.

Solution:

∵ LCM × GCF = 15 × 21
⇒ GCF(15, 21) = (15 × 21)/105 = 3
Therefore, the greatest common factor of 15 and 21 is 3.
Example 2: Find the greatest number that divides 15 and 21 exactly.

Solution:

The greatest number that divides 15 and 21 exactly is their greatest common factor, i.e. GCF of 15 and 21.
⇒ Factors of 15 and 21:
- Factors of 15 = 1, 3, 5, 15
- Factors of 21 = 1, 3, 7, 21
Therefore, the GCF of 15 and 21 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 105. If one number is 15, find the other number.

Solution:

Given: GCF (x, 15) = 3 and LCM (x, 15) = 105
∵ GCF × LCM = 15 × (x)
⇒ x = (GCF × LCM)/15
⇒ x = (3 × 105)/15
⇒ x = 21
Therefore, the other number is 21.

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FAQs on GCF of 15 and 21

What is the GCF of 15 and 21?

The GCF of 15 and 21 is 3. To calculate the greatest common factor (GCF) of 15 and 21, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 21 = 1, 3, 7, 21) and choose the greatest factor that exactly divides both 15 and 21, i.e., 3.

How to Find the GCF of 15 and 21 by Long Division Method?

To find the GCF of 15, 21 using long division method, 21 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

How to Find the GCF of 15 and 21 by Prime Factorization?

To find the GCF of 15 and 21, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 21 = 3 × 7.
⇒ Since 3 is the only common prime factor of 15 and 21. Hence, GCF (15, 21) = 3.
☛ What is a Prime Number?

What are the Methods to Find GCF of 15 and 21?

There are three commonly used methods to find the GCF of 15 and 21.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 21 and 15 is 3, Find its LCM.

GCF(21, 15) × LCM(21, 15) = 21 × 15
Since the GCF of 21 and 15 = 3
⇒ 3 × LCM(21, 15) = 315
Therefore, LCM = 105
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 15, 21?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 21, i.e. GCF × LCM = 15 × 21.

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