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HCF of 63 and 84

HCF of 63 and 84 is the largest possible number that divides 63 and 84 exactly without any remainder. The factors of 63 and 84 are 1, 3, 7, 9, 21, 63 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 commonly used methods to find the HCF of 63 and 84 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 63 and 84
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 63 and 84?

Answer: HCF of 63 and 84 is 21.

Explanation:

The HCF of two non-zero integers, x(63) and y(84), is the highest positive integer m(21) that divides both x(63) and y(84) without any remainder.

Methods to Find HCF of 63 and 84

The methods to find the HCF of 63 and 84 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 63 and 84 by Prime Factorization

Prime factorization of 63 and 84 is (3 × 3 × 7) and (2 × 2 × 3 × 7) respectively. As visible, 63 and 84 have common prime factors. Hence, the HCF of 63 and 84 is 3 × 7 = 21.

HCF of 63 and 84 by Long Division

HCF of 63 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 84 (larger number) by 63 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (63) by the remainder (21).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (21) is the HCF of 63 and 84.

HCF of 63 and 84 by Listing Common Factors

Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

There are 4 common factors of 63 and 84, that are 1, 3, 21, and 7. Therefore, the highest common factor of 63 and 84 is 21.

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HCF of 63 and 84 Examples

Example 1: For two numbers, HCF = 21 and LCM = 252. If one number is 63, find the other number.

Solution:

Given: HCF (y, 63) = 21 and LCM (y, 63) = 252
∵ HCF × LCM = 63 × (y)
⇒ y = (HCF × LCM)/63
⇒ y = (21 × 252)/63
⇒ y = 84
Therefore, the other number is 84.
Example 2: Find the highest number that divides 63 and 84 exactly.

Solution:

The highest number that divides 63 and 84 exactly is their highest common factor, i.e. HCF of 63 and 84.
⇒ Factors of 63 and 84:
- Factors of 63 = 1, 3, 7, 9, 21, 63
- Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, the HCF of 63 and 84 is 21.
Example 3: Find the HCF of 63 and 84, if their LCM is 252.

Solution:

∵ LCM × HCF = 63 × 84
⇒ HCF(63, 84) = (63 × 84)/252 = 21
Therefore, the highest common factor of 63 and 84 is 21.

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FAQs on HCF of 63 and 84

What is the HCF of 63 and 84?

The HCF of 63 and 84 is 21. To calculate the HCF (Highest Common Factor) of 63 and 84, we need to factor each number (factors of 63 = 1, 3, 7, 9, 21, 63; factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and choose the highest factor that exactly divides both 63 and 84, i.e., 21.

What are the Methods to Find HCF of 63 and 84?

There are three commonly used methods to find the HCF of 63 and 84.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the HCF of 63 and 84 by Prime Factorization?

To find the HCF of 63 and 84, we will find the prime factorization of the given numbers, i.e. 63 = 3 × 3 × 7; 84 = 2 × 2 × 3 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 63 and 84. Hence, HCF(63, 84) = 3 × 7 = 21
☛ What are Prime Numbers?

How to Find the HCF of 63 and 84 by Long Division Method?

To find the HCF of 63, 84 using long division method, 84 is divided by 63. The corresponding divisor (21) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 63, 84?

The following equation can be used to express the relation between LCM and HCF of 63 and 84, i.e. HCF × LCM = 63 × 84.

If the HCF of 84 and 63 is 21, Find its LCM.

HCF(84, 63) × LCM(84, 63) = 84 × 63
Since the HCF of 84 and 63 = 21
⇒ 21 × LCM(84, 63) = 5292
Therefore, LCM = 252
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