Highest Common Factor of 697, 975 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, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 697, 975 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, 975 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, 975 is 1.

HCF(697, 975) = 1

HCF of 697, 975 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, 975 is 1.

Highest Common Factor of 697,975 using Euclid's algorithm

Highest Common Factor of 697,975 is 1

Step 1: Since 975 > 697, we apply the division lemma to 975 and 697, to get

975 = 697 x 1 + 278

Step 2: Since the reminder 697 ≠ 0, we apply division lemma to 278 and 697, to get

697 = 278 x 2 + 141

Step 3: We consider the new divisor 278 and the new remainder 141, and apply the division lemma to get

278 = 141 x 1 + 137

We consider the new divisor 141 and the new remainder 137,and apply the division lemma to get

141 = 137 x 1 + 4

We consider the new divisor 137 and the new remainder 4,and apply the division lemma to get

137 = 4 x 34 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 697 and 975 is 1

Notice that 1 = HCF(4,1) = HCF(137,4) = HCF(141,137) = HCF(278,141) = HCF(697,278) = HCF(975,697) .

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Frequently Asked Questions on HCF of 697, 975 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, 975?

Answer: HCF of 697, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 697, 975 using Euclid's Algorithm?

Answer: For arbitrary numbers 697, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.