Highest Common Factor of 336, 542, 364 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 336, 542, 364 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 336, 542, 364 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 336, 542, 364 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 336, 542, 364 is 2.

HCF(336, 542, 364) = 2

HCF of 336, 542, 364 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 336, 542, 364 is 2.

Highest Common Factor of 336,542,364 using Euclid's algorithm

Highest Common Factor of 336,542,364 is 2

Step 1: Since 542 > 336, we apply the division lemma to 542 and 336, to get

542 = 336 x 1 + 206

Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 206 and 336, to get

336 = 206 x 1 + 130

Step 3: We consider the new divisor 206 and the new remainder 130, and apply the division lemma to get

206 = 130 x 1 + 76

We consider the new divisor 130 and the new remainder 76,and apply the division lemma to get

130 = 76 x 1 + 54

We consider the new divisor 76 and the new remainder 54,and apply the division lemma to get

76 = 54 x 1 + 22

We consider the new divisor 54 and the new remainder 22,and apply the division lemma to get

54 = 22 x 2 + 10

We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get

22 = 10 x 2 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 336 and 542 is 2

Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(54,22) = HCF(76,54) = HCF(130,76) = HCF(206,130) = HCF(336,206) = HCF(542,336) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 364 > 2, we apply the division lemma to 364 and 2, to get

364 = 2 x 182 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 364 is 2

Notice that 2 = HCF(364,2) .

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Frequently Asked Questions on HCF of 336, 542, 364 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 336, 542, 364?

Answer: HCF of 336, 542, 364 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 336, 542, 364 using Euclid's Algorithm?

Answer: For arbitrary numbers 336, 542, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.