Highest Common Factor of 340, 516, 642 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 340, 516, 642 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 340, 516, 642 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 340, 516, 642 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 340, 516, 642 is 2.

HCF(340, 516, 642) = 2

HCF of 340, 516, 642 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 340, 516, 642 is 2.

Highest Common Factor of 340,516,642 using Euclid's algorithm

Highest Common Factor of 340,516,642 is 2

Step 1: Since 516 > 340, we apply the division lemma to 516 and 340, to get

516 = 340 x 1 + 176

Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 176 and 340, to get

340 = 176 x 1 + 164

Step 3: We consider the new divisor 176 and the new remainder 164, and apply the division lemma to get

176 = 164 x 1 + 12

We consider the new divisor 164 and the new remainder 12,and apply the division lemma to get

164 = 12 x 13 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 340 and 516 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(164,12) = HCF(176,164) = HCF(340,176) = HCF(516,340) .

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

Step 1: Since 642 > 4, we apply the division lemma to 642 and 4, to get

642 = 4 x 160 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 642 is 2

Notice that 2 = HCF(4,2) = HCF(642,4) .

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Frequently Asked Questions on HCF of 340, 516, 642 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 340, 516, 642?

Answer: HCF of 340, 516, 642 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 340, 516, 642 using Euclid's Algorithm?

Answer: For arbitrary numbers 340, 516, 642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.