Highest Common Factor of 471, 688, 535 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 471, 688, 535 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 471, 688, 535 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 471, 688, 535 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 471, 688, 535 is 1.

HCF(471, 688, 535) = 1

HCF of 471, 688, 535 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 471, 688, 535 is 1.

Highest Common Factor of 471,688,535 using Euclid's algorithm

Highest Common Factor of 471,688,535 is 1

Step 1: Since 688 > 471, we apply the division lemma to 688 and 471, to get

688 = 471 x 1 + 217

Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 217 and 471, to get

471 = 217 x 2 + 37

Step 3: We consider the new divisor 217 and the new remainder 37, and apply the division lemma to get

217 = 37 x 5 + 32

We consider the new divisor 37 and the new remainder 32,and apply the division lemma to get

37 = 32 x 1 + 5

We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get

32 = 5 x 6 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 471 and 688 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(37,32) = HCF(217,37) = HCF(471,217) = HCF(688,471) .

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

Step 1: Since 535 > 1, we apply the division lemma to 535 and 1, to get

535 = 1 x 535 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 535 is 1

Notice that 1 = HCF(535,1) .

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Frequently Asked Questions on HCF of 471, 688, 535 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 471, 688, 535?

Answer: HCF of 471, 688, 535 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 471, 688, 535 using Euclid's Algorithm?

Answer: For arbitrary numbers 471, 688, 535 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.