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 nonzero 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.
☛ Also Check:
 HCF of 2, 3 and 4 = 1
 HCF of 2 and 5 = 1
 HCF of 8 and 12 = 4
 HCF of 27 and 45 = 9
 HCF of 18 and 60 = 6
 HCF of 6, 72 and 120 = 6
 HCF of 2, 4 and 8 = 2
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.
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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