Highest Common Factor of 600, 821, 371 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 600, 821, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 600, 821, 371 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 600, 821, 371 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 600, 821, 371 is 1.

HCF(600, 821, 371) = 1

HCF of 600, 821, 371 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 600, 821, 371 is 1.

Highest Common Factor of 600,821,371 using Euclid's algorithm

Highest Common Factor of 600,821,371 is 1

Step 1: Since 821 > 600, we apply the division lemma to 821 and 600, to get

821 = 600 x 1 + 221

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 221 and 600, to get

600 = 221 x 2 + 158

Step 3: We consider the new divisor 221 and the new remainder 158, and apply the division lemma to get

221 = 158 x 1 + 63

We consider the new divisor 158 and the new remainder 63,and apply the division lemma to get

158 = 63 x 2 + 32

We consider the new divisor 63 and the new remainder 32,and apply the division lemma to get

63 = 32 x 1 + 31

We consider the new divisor 32 and the new remainder 31,and apply the division lemma to get

32 = 31 x 1 + 1

We consider the new divisor 31 and the new remainder 1,and apply the division lemma to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 600 and 821 is 1

Notice that 1 = HCF(31,1) = HCF(32,31) = HCF(63,32) = HCF(158,63) = HCF(221,158) = HCF(600,221) = HCF(821,600) .

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

Step 1: Since 371 > 1, we apply the division lemma to 371 and 1, to get

371 = 1 x 371 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 371 is 1

Notice that 1 = HCF(371,1) .

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Frequently Asked Questions on HCF of 600, 821, 371 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 600, 821, 371?

Answer: HCF of 600, 821, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 600, 821, 371 using Euclid's Algorithm?

Answer: For arbitrary numbers 600, 821, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.