Highest Common Factor of 354, 640, 616 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 354, 640, 616 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 354, 640, 616 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 354, 640, 616 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 354, 640, 616 is 2.

HCF(354, 640, 616) = 2

HCF of 354, 640, 616 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 354, 640, 616 is 2.

Highest Common Factor of 354,640,616 using Euclid's algorithm

Highest Common Factor of 354,640,616 is 2

Step 1: Since 640 > 354, we apply the division lemma to 640 and 354, to get

640 = 354 x 1 + 286

Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 286 and 354, to get

354 = 286 x 1 + 68

Step 3: We consider the new divisor 286 and the new remainder 68, and apply the division lemma to get

286 = 68 x 4 + 14

We consider the new divisor 68 and the new remainder 14,and apply the division lemma to get

68 = 14 x 4 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 640 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(68,14) = HCF(286,68) = HCF(354,286) = HCF(640,354) .

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

Step 1: Since 616 > 2, we apply the division lemma to 616 and 2, to get

616 = 2 x 308 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 616 is 2

Notice that 2 = HCF(616,2) .

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Frequently Asked Questions on HCF of 354, 640, 616 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 354, 640, 616?

Answer: HCF of 354, 640, 616 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 354, 640, 616 using Euclid's Algorithm?

Answer: For arbitrary numbers 354, 640, 616 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.