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HCF of 336, 240 and 96

HCF of 336, 240 and 96 is the largest possible number that divides 336, 240 and 96 exactly without any remainder. The factors of 336, 240 and 96 are (1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336), (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240) and (1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) respectively. There are 3 commonly used methods to find the HCF of 336, 240 and 96 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 336, 240 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 336, 240 and 96?

Answer: HCF of 336, 240 and 96 is 48.

Explanation:

The HCF of three non-zero integers, x(336), y(240) and z(96), is the highest positive integer m(48) that divides x(336), y(240) and z(96) without any remainder.

Methods to Find HCF of 336, 240 and 96

The methods to find the HCF of 336, 240 and 96 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

HCF of 336, 240 and 96 by Listing Common Factors

Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
Factors of 240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 10 common factors of 336, 240 and 96, that are 1, 2, 3, 4, 6, 8, 12, 16, 48, and 24. Therefore, the highest common factor of 336, 240 and 96 is 48.

HCF of 336, 240 and 96 by Prime Factorization

Prime factorization of 336, 240 and 96 is (2 × 2 × 2 × 2 × 3 × 7), (2 × 2 × 2 × 2 × 3 × 5) and (2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 336, 240 and 96 have common prime factors. Hence, the HCF of 336, 240 and 96 is 2 × 2 × 2 × 2 × 3 = 48.

HCF of 336, 240 and 96 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(336, 240, 96) = HCF(HCF(336, 240), 96)

HCF(336, 240) = HCF(240, 336 mod 240) = HCF(240, 96)
HCF(240, 96) = HCF(96, 240 mod 96) = HCF(96, 48)
HCF(96, 48) = HCF(48, 96 mod 48) = HCF(48, 0)
HCF(48, 0) = 48 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(48, 96)

HCF(96, 48) = HCF(48, 96 mod 48) = HCF(48, 0)
HCF(48, 0) = 48 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 336, 240 and 96 is 48.

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HCF of 336, 240 and 96 Examples

Example 1: Calculate the HCF of 336, 240, and 96 using LCM of the given numbers.

Solution:

Prime factorization of 336, 240 and 96 is given as,
- 336 = 2 × 2 × 2 × 2 × 3 × 7
- 240 = 2 × 2 × 2 × 2 × 3 × 5
- 96 = 2 × 2 × 2 × 2 × 2 × 3
LCM(336, 240) = 1680, LCM(240, 96) = 480, LCM(96, 336) = 672, LCM(336, 240, 96) = 3360
⇒ HCF(336, 240, 96) = [(336 × 240 × 96) × LCM(336, 240, 96)]/[LCM(336, 240) × LCM (240, 96) × LCM(96, 336)]
⇒ HCF(336, 240, 96) = (7741440 × 3360)/(1680 × 480 × 672)
⇒ HCF(336, 240, 96) = 48.
Therefore, the HCF of 336, 240 and 96 is 48.
Example 2: Find the highest number that divides 336, 240, and 96 completely.

Solution:

The highest number that divides 336, 240, and 96 exactly is their highest common factor.
- Factors of 336 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
- Factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The HCF of 336, 240, and 96 is 48.
∴ The highest number that divides 336, 240, and 96 is 48.
Example 3: Verify the relation between the LCM and HCF of 336, 240 and 96.

Solution:

The relation between the LCM and HCF of 336, 240 and 96 is given as, HCF(336, 240, 96) = [(336 × 240 × 96) × LCM(336, 240, 96)]/[LCM(336, 240) × LCM (240, 96) × LCM(336, 96)]
⇒ Prime factorization of 336, 240 and 96:
- 336 = 2 × 2 × 2 × 2 × 3 × 7
- 240 = 2 × 2 × 2 × 2 × 3 × 5
- 96 = 2 × 2 × 2 × 2 × 2 × 3
∴ LCM of (336, 240), (240, 96), (336, 96), and (336, 240, 96) is 1680, 480, 672, and 3360 respectively.
Now, LHS = HCF(336, 240, 96) = 48.
And, RHS = [(336 × 240 × 96) × LCM(336, 240, 96)]/[LCM(336, 240) × LCM (240, 96) × LCM(336, 96)] = [(7741440) × 3360]/[1680 × 480 × 672]
LHS = RHS = 48.
Hence verified.

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FAQs on HCF of 336, 240 and 96

What is the HCF of 336, 240 and 96?

The HCF of 336, 240 and 96 is 48. To calculate the highest common factor of 336, 240 and 96, we need to factor each number (factors of 336 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336; factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the highest factor that exactly divides 336, 240 and 96, i.e., 48.

Which of the following is HCF of 336, 240 and 96? 48, 361, 350, 367, 343, 365, 339

HCF of 336, 240, 96 will be the number that divides 336, 240, and 96 without leaving any remainder. The only number that satisfies the given condition is 48.

What are the Methods to Find HCF of 336, 240 and 96?

There are three commonly used methods to find the HCF of 336, 240 and 96.

By Listing Common Factors
By Long Division
By Prime Factorization

What is the Relation Between LCM and HCF of 336, 240 and 96?

The following equation can be used to express the relation between LCM and HCF of 336, 240 and 96, i.e. HCF(336, 240, 96) = [(336 × 240 × 96) × LCM(336, 240, 96)]/[LCM(336, 240) × LCM (240, 96) × LCM(336, 96)].
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How to Find the HCF of 336, 240 and 96 by Prime Factorization?

To find the HCF of 336, 240 and 96, we will find the prime factorization of given numbers, i.e. 336 = 2 × 2 × 2 × 2 × 3 × 7; 240 = 2 × 2 × 2 × 2 × 3 × 5; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 2, 3 are common terms in the prime factorization of 336, 240 and 96. Hence, HCF(336, 240, 96) = 2 × 2 × 2 × 2 × 3 = 48
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