Highest Common Factor of 321, 197, 696, 516 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 321, 197, 696, 516 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 321, 197, 696, 516 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 321, 197, 696, 516 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 321, 197, 696, 516 is 1.

HCF(321, 197, 696, 516) = 1

HCF of 321, 197, 696, 516 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 321, 197, 696, 516 is 1.

Highest Common Factor of 321,197,696,516 using Euclid's algorithm

Highest Common Factor of 321,197,696,516 is 1

Step 1: Since 321 > 197, we apply the division lemma to 321 and 197, to get

321 = 197 x 1 + 124

Step 2: Since the reminder 197 ≠ 0, we apply division lemma to 124 and 197, to get

197 = 124 x 1 + 73

Step 3: We consider the new divisor 124 and the new remainder 73, and apply the division lemma to get

124 = 73 x 1 + 51

We consider the new divisor 73 and the new remainder 51,and apply the division lemma to get

73 = 51 x 1 + 22

We consider the new divisor 51 and the new remainder 22,and apply the division lemma to get

51 = 22 x 2 + 7

We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get

22 = 7 x 3 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 321 and 197 is 1

Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(51,22) = HCF(73,51) = HCF(124,73) = HCF(197,124) = HCF(321,197) .

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

Step 1: Since 696 > 1, we apply the division lemma to 696 and 1, to get

696 = 1 x 696 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 696 is 1

Notice that 1 = HCF(696,1) .

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

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

516 = 1 x 516 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 516 is 1

Notice that 1 = HCF(516,1) .

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Frequently Asked Questions on HCF of 321, 197, 696, 516 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 321, 197, 696, 516?

Answer: HCF of 321, 197, 696, 516 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 321, 197, 696, 516 using Euclid's Algorithm?

Answer: For arbitrary numbers 321, 197, 696, 516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.