Highest Common Factor of 470, 857, 698 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 470, 857, 698 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 470, 857, 698 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 470, 857, 698 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 470, 857, 698 is 1.

HCF(470, 857, 698) = 1

HCF of 470, 857, 698 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 470, 857, 698 is 1.

Highest Common Factor of 470,857,698 using Euclid's algorithm

Highest Common Factor of 470,857,698 is 1

Step 1: Since 857 > 470, we apply the division lemma to 857 and 470, to get

857 = 470 x 1 + 387

Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 387 and 470, to get

470 = 387 x 1 + 83

Step 3: We consider the new divisor 387 and the new remainder 83, and apply the division lemma to get

387 = 83 x 4 + 55

We consider the new divisor 83 and the new remainder 55,and apply the division lemma to get

83 = 55 x 1 + 28

We consider the new divisor 55 and the new remainder 28,and apply the division lemma to get

55 = 28 x 1 + 27

We consider the new divisor 28 and the new remainder 27,and apply the division lemma to get

28 = 27 x 1 + 1

We consider the new divisor 27 and the new remainder 1,and apply the division lemma to get

27 = 1 x 27 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 470 and 857 is 1

Notice that 1 = HCF(27,1) = HCF(28,27) = HCF(55,28) = HCF(83,55) = HCF(387,83) = HCF(470,387) = HCF(857,470) .

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

Step 1: Since 698 > 1, we apply the division lemma to 698 and 1, to get

698 = 1 x 698 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 698 is 1

Notice that 1 = HCF(698,1) .

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Frequently Asked Questions on HCF of 470, 857, 698 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 470, 857, 698?

Answer: HCF of 470, 857, 698 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 470, 857, 698 using Euclid's Algorithm?

Answer: For arbitrary numbers 470, 857, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.