Highest Common Factor of 697, 851, 74 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 697, 851, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 697, 851, 74 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 697, 851, 74 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 697, 851, 74 is 1.

HCF(697, 851, 74) = 1

HCF of 697, 851, 74 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 697, 851, 74 is 1.

Highest Common Factor of 697,851,74 using Euclid's algorithm

Highest Common Factor of 697,851,74 is 1

Step 1: Since 851 > 697, we apply the division lemma to 851 and 697, to get

851 = 697 x 1 + 154

Step 2: Since the reminder 697 ≠ 0, we apply division lemma to 154 and 697, to get

697 = 154 x 4 + 81

Step 3: We consider the new divisor 154 and the new remainder 81, and apply the division lemma to get

154 = 81 x 1 + 73

We consider the new divisor 81 and the new remainder 73,and apply the division lemma to get

81 = 73 x 1 + 8

We consider the new divisor 73 and the new remainder 8,and apply the division lemma to get

73 = 8 x 9 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 697 and 851 is 1

Notice that 1 = HCF(8,1) = HCF(73,8) = HCF(81,73) = HCF(154,81) = HCF(697,154) = HCF(851,697) .

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

Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get

74 = 1 x 74 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1

Notice that 1 = HCF(74,1) .

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Frequently Asked Questions on HCF of 697, 851, 74 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 697, 851, 74?

Answer: HCF of 697, 851, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 697, 851, 74 using Euclid's Algorithm?

Answer: For arbitrary numbers 697, 851, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.