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HCF of 36, 42 and 48

HCF of 36, 42 and 48 is the largest possible number that divides 36, 42 and 48 exactly without any remainder. The factors of 36, 42 and 48 are (1, 2, 3, 4, 6, 9, 12, 18, 36), (1, 2, 3, 6, 7, 14, 21, 42) and (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) respectively. There are 3 commonly used methods to find the HCF of 36, 42 and 48 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 36, 42 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 36, 42 and 48?

Answer: HCF of 36, 42 and 48 is 6.

Explanation:

The HCF of three non-zero integers, x(36), y(42) and z(48), is the highest positive integer m(6) that divides x(36), y(42) and z(48) without any remainder.

Methods to Find HCF of 36, 42 and 48

Let's look at the different methods for finding the HCF of 36, 42 and 48.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

HCF of 36, 42 and 48 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 4 common factors of 36, 42 and 48, that are 1, 2, 3, and 6. Therefore, the highest common factor of 36, 42 and 48 is 6.

HCF of 36, 42 and 48 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

HCF(36, 42, 48) = HCF(HCF(36, 42), 48)

HCF(42, 36) = HCF(36, 42 mod 36) = HCF(36, 6)
HCF(36, 6) = HCF(6, 36 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(6, 48)

HCF(48, 6) = HCF(6, 48 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 36, 42 and 48 is 6.

HCF of 36, 42 and 48 by Long Division

HCF of 36, 42 and 48 can be represented as HCF of (HCF of 36, 42) and 48. HCF(36, 42, 48) can be thus calculated by first finding HCF(36, 42) using long division and thereafter using this result with 48 to perform long division again.

Step 1: Divide 42 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (6). Repeat this process until the remainder = 0.
⇒ HCF(36, 42) = 6.
Step 3: Now to find the HCF of 6 and 48, we will perform a long division on 48 and 6.
Step 4: For remainder = 0, divisor = 6 ⇒ HCF(6, 48) = 6

Thus, HCF(36, 42, 48) = HCF(HCF(36, 42), 48) = 6.

☛ Also Check:

HCF of 36, 42 and 48 Examples

Example 1: Calculate the HCF of 36, 42, and 48 using LCM of the given numbers.

Solution:

Prime factorization of 36, 42 and 48 is given as,
- 36 = 2 × 2 × 3 × 3
- 42 = 2 × 3 × 7
- 48 = 2 × 2 × 2 × 2 × 3
LCM(36, 42) = 252, LCM(42, 48) = 336, LCM(48, 36) = 144, LCM(36, 42, 48) = 1008
⇒ HCF(36, 42, 48) = [(36 × 42 × 48) × LCM(36, 42, 48)]/[LCM(36, 42) × LCM (42, 48) × LCM(48, 36)]
⇒ HCF(36, 42, 48) = (72576 × 1008)/(252 × 336 × 144)
⇒ HCF(36, 42, 48) = 6.
Therefore, the HCF of 36, 42 and 48 is 6.
Example 2: Find the highest number that divides 36, 42, and 48 completely.

Solution:

The highest number that divides 36, 42, and 48 exactly is their highest common factor.
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The HCF of 36, 42, and 48 is 6.
∴ The highest number that divides 36, 42, and 48 is 6.
Example 3: Verify the relation between the LCM and HCF of 36, 42 and 48.

Solution:

The relation between the LCM and HCF of 36, 42 and 48 is given as, HCF(36, 42, 48) = [(36 × 42 × 48) × LCM(36, 42, 48)]/[LCM(36, 42) × LCM (42, 48) × LCM(36, 48)]
⇒ Prime factorization of 36, 42 and 48:
- 36 = 2 × 2 × 3 × 3
- 42 = 2 × 3 × 7
- 48 = 2 × 2 × 2 × 2 × 3
∴ LCM of (36, 42), (42, 48), (36, 48), and (36, 42, 48) is 252, 336, 144, and 1008 respectively.
Now, LHS = HCF(36, 42, 48) = 6.
And, RHS = [(36 × 42 × 48) × LCM(36, 42, 48)]/[LCM(36, 42) × LCM (42, 48) × LCM(36, 48)] = [(72576) × 1008]/[252 × 336 × 144]
LHS = RHS = 6.
Hence verified.

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FAQs on HCF of 36, 42 and 48

What is the HCF of 36, 42 and 48?

The HCF of 36, 42 and 48 is 6. To calculate the HCF (Highest Common Factor) of 36, 42 and 48, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the highest factor that exactly divides 36, 42 and 48, i.e., 6.

What are the Methods to Find HCF of 36, 42 and 48?

There are three commonly used methods to find the HCF of 36, 42 and 48.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the HCF of 36, 42 and 48 by Prime Factorization?

To find the HCF of 36, 42 and 48, we will find the prime factorization of given numbers, i.e. 36 = 2 × 2 × 3 × 3; 42 = 2 × 3 × 7; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 36, 42 and 48. Hence, HCF(36, 42, 48) = 2 × 3 = 6
☛ What is a Prime Number?

Which of the following is HCF of 36, 42 and 48? 6, 83, 95, 57, 72

HCF of 36, 42, 48 will be the number that divides 36, 42, and 48 without leaving any remainder. The only number that satisfies the given condition is 6.

What is the Relation Between LCM and HCF of 36, 42 and 48?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 36, 42 and 48, i.e. HCF(36, 42, 48) = [(36 × 42 × 48) × LCM(36, 42, 48)]/[LCM(36, 42) × LCM (42, 48) × LCM(36, 48)].
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