Highest Common Factor of 609, 821, 908 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 609, 821, 908 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 609, 821, 908 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 609, 821, 908 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 609, 821, 908 is 1.

HCF(609, 821, 908) = 1

HCF of 609, 821, 908 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 609, 821, 908 is 1.

Highest Common Factor of 609,821,908 using Euclid's algorithm

Highest Common Factor of 609,821,908 is 1

Step 1: Since 821 > 609, we apply the division lemma to 821 and 609, to get

821 = 609 x 1 + 212

Step 2: Since the reminder 609 ≠ 0, we apply division lemma to 212 and 609, to get

609 = 212 x 2 + 185

Step 3: We consider the new divisor 212 and the new remainder 185, and apply the division lemma to get

212 = 185 x 1 + 27

We consider the new divisor 185 and the new remainder 27,and apply the division lemma to get

185 = 27 x 6 + 23

We consider the new divisor 27 and the new remainder 23,and apply the division lemma to get

27 = 23 x 1 + 4

We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get

23 = 4 x 5 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 609 and 821 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(27,23) = HCF(185,27) = HCF(212,185) = HCF(609,212) = HCF(821,609) .

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

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

908 = 1 x 908 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 908 is 1

Notice that 1 = HCF(908,1) .

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Frequently Asked Questions on HCF of 609, 821, 908 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 609, 821, 908?

Answer: HCF of 609, 821, 908 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 609, 821, 908 using Euclid's Algorithm?

Answer: For arbitrary numbers 609, 821, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.