Highest Common Factor of 968, 340, 341 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 968, 340, 341 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 968, 340, 341 is 1 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 968, 340, 341 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 968, 340, 341 is 1.

HCF(968, 340, 341) = 1

HCF of 968, 340, 341 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 968, 340, 341 is 1.

Highest Common Factor of 968,340,341 using Euclid's algorithm

Highest Common Factor of 968,340,341 is 1

Step 1: Since 968 > 340, we apply the division lemma to 968 and 340, to get

968 = 340 x 2 + 288

Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 288 and 340, to get

340 = 288 x 1 + 52

Step 3: We consider the new divisor 288 and the new remainder 52, and apply the division lemma to get

288 = 52 x 5 + 28

We consider the new divisor 52 and the new remainder 28,and apply the division lemma to get

52 = 28 x 1 + 24

We consider the new divisor 28 and the new remainder 24,and apply the division lemma to get

28 = 24 x 1 + 4

We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get

24 = 4 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 968 and 340 is 4

Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(52,28) = HCF(288,52) = HCF(340,288) = HCF(968,340) .

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

Step 1: Since 341 > 4, we apply the division lemma to 341 and 4, to get

341 = 4 x 85 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 341 is 1

Notice that 1 = HCF(4,1) = HCF(341,4) .

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Frequently Asked Questions on HCF of 968, 340, 341 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 968, 340, 341?

Answer: HCF of 968, 340, 341 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 968, 340, 341 using Euclid's Algorithm?

Answer: For arbitrary numbers 968, 340, 341 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.