Highest Common Factor of 696, 908, 403 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 696, 908, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 696, 908, 403 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 696, 908, 403 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 696, 908, 403 is 1.

HCF(696, 908, 403) = 1

HCF of 696, 908, 403 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 696, 908, 403 is 1.

Highest Common Factor of 696,908,403 using Euclid's algorithm

Highest Common Factor of 696,908,403 is 1

Step 1: Since 908 > 696, we apply the division lemma to 908 and 696, to get

908 = 696 x 1 + 212

Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 212 and 696, to get

696 = 212 x 3 + 60

Step 3: We consider the new divisor 212 and the new remainder 60, and apply the division lemma to get

212 = 60 x 3 + 32

We consider the new divisor 60 and the new remainder 32,and apply the division lemma to get

60 = 32 x 1 + 28

We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get

32 = 28 x 1 + 4

We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 696 and 908 is 4

Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(60,32) = HCF(212,60) = HCF(696,212) = HCF(908,696) .

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

Step 1: Since 403 > 4, we apply the division lemma to 403 and 4, to get

403 = 4 x 100 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 403 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(403,4) .

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Frequently Asked Questions on HCF of 696, 908, 403 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 696, 908, 403?

Answer: HCF of 696, 908, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 696, 908, 403 using Euclid's Algorithm?

Answer: For arbitrary numbers 696, 908, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.