HCF of 36 and 63
HCF of 36 and 63 is the largest possible number that divides 36 and 63 exactly without any remainder. The factors of 36 and 63 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the HCF of 36 and 63  Euclidean algorithm, prime factorization, and long division.
1.  HCF of 36 and 63 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 36 and 63?
Answer: HCF of 36 and 63 is 9.
Explanation:
The HCF of two nonzero integers, x(36) and y(63), is the highest positive integer m(9) that divides both x(36) and y(63) without any remainder.
Methods to Find HCF of 36 and 63
Let's look at the different methods for finding the HCF of 36 and 63.
 Long Division Method
 Prime Factorization Method
 Listing Common Factors
HCF of 36 and 63 by Long Division
HCF of 36 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 63 (larger number) by 36 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (27).
 Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (9) is the HCF of 36 and 63.
HCF of 36 and 63 by Prime Factorization
Prime factorization of 36 and 63 is (2 × 2 × 3 × 3) and (3 × 3 × 7) respectively. As visible, 36 and 63 have common prime factors. Hence, the HCF of 36 and 63 is 3 × 3 = 9.
HCF of 36 and 63 by Listing Common Factors
 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 63: 1, 3, 7, 9, 21, 63
There are 3 common factors of 36 and 63, that are 1, 3, and 9. Therefore, the highest common factor of 36 and 63 is 9.
☛ Also Check:
 HCF of 6 and 10 = 2
 HCF of 4 and 16 = 4
 HCF of 14 and 15 = 1
 HCF of 12, 45 and 75 = 3
 HCF of 6 and 8 = 2
 HCF of 45 and 180 = 45
 HCF of 2 and 3 = 1
HCF of 36 and 63 Examples

Example 1: The product of two numbers is 2268. If their HCF is 9, what is their LCM?
Solution:
Given: HCF = 9 and product of numbers = 2268
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 2268/9
Therefore, the LCM is 252. 
Example 2: For two numbers, HCF = 9 and LCM = 252. If one number is 36, find the other number.
Solution:
Given: HCF (x, 36) = 9 and LCM (x, 36) = 252
∵ HCF × LCM = 36 × (x)
⇒ x = (HCF × LCM)/36
⇒ x = (9 × 252)/36
⇒ x = 63
Therefore, the other number is 63. 
Example 3: Find the highest number that divides 36 and 63 exactly.
Solution:
The highest number that divides 36 and 63 exactly is their highest common factor, i.e. HCF of 36 and 63.
⇒ Factors of 36 and 63: Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 63 = 1, 3, 7, 9, 21, 63
Therefore, the HCF of 36 and 63 is 9.
FAQs on HCF of 36 and 63
What is the HCF of 36 and 63?
The HCF of 36 and 63 is 9. To calculate the Highest common factor of 36 and 63, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the highest factor that exactly divides both 36 and 63, i.e., 9.
What is the Relation Between LCM and HCF of 36, 63?
The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 36 and 63, i.e. HCF × LCM = 36 × 63.
How to Find the HCF of 36 and 63 by Long Division Method?
To find the HCF of 36, 63 using long division method, 63 is divided by 36. The corresponding divisor (9) when remainder equals 0 is taken as HCF.
How to Find the HCF of 36 and 63 by Prime Factorization?
To find the HCF of 36 and 63, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 63 = 3 × 3 × 7.
⇒ Since 3, 3 are common terms in the prime factorization of 36 and 63. Hence, HCF(36, 63) = 3 × 3 = 9
☛ What are Prime Numbers?
If the HCF of 63 and 36 is 9, Find its LCM.
HCF(63, 36) × LCM(63, 36) = 63 × 36
Since the HCF of 63 and 36 = 9
⇒ 9 × LCM(63, 36) = 2268
Therefore, LCM = 252
☛ Highest Common Factor Calculator
What are the Methods to Find HCF of 36 and 63?
There are three commonly used methods to find the HCF of 36 and 63.
 By Long Division
 By Prime Factorization
 By Listing Common Factors
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