Highest Common Factor of 694, 420, 951 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 694, 420, 951 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 694, 420, 951 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 694, 420, 951 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 694, 420, 951 is 1.

HCF(694, 420, 951) = 1

HCF of 694, 420, 951 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 694, 420, 951 is 1.

Highest Common Factor of 694,420,951 using Euclid's algorithm

Highest Common Factor of 694,420,951 is 1

Step 1: Since 694 > 420, we apply the division lemma to 694 and 420, to get

694 = 420 x 1 + 274

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 274 and 420, to get

420 = 274 x 1 + 146

Step 3: We consider the new divisor 274 and the new remainder 146, and apply the division lemma to get

274 = 146 x 1 + 128

We consider the new divisor 146 and the new remainder 128,and apply the division lemma to get

146 = 128 x 1 + 18

We consider the new divisor 128 and the new remainder 18,and apply the division lemma to get

128 = 18 x 7 + 2

We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get

18 = 2 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 694 and 420 is 2

Notice that 2 = HCF(18,2) = HCF(128,18) = HCF(146,128) = HCF(274,146) = HCF(420,274) = HCF(694,420) .

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

Step 1: Since 951 > 2, we apply the division lemma to 951 and 2, to get

951 = 2 x 475 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 951 is 1

Notice that 1 = HCF(2,1) = HCF(951,2) .

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Frequently Asked Questions on HCF of 694, 420, 951 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 694, 420, 951?

Answer: HCF of 694, 420, 951 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 694, 420, 951 using Euclid's Algorithm?

Answer: For arbitrary numbers 694, 420, 951 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.