Highest Common Factor of 967, 600, 821 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 967, 600, 821 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 967, 600, 821 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 967, 600, 821 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 967, 600, 821 is 1.

HCF(967, 600, 821) = 1

HCF of 967, 600, 821 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 967, 600, 821 is 1.

Highest Common Factor of 967,600,821 using Euclid's algorithm

Highest Common Factor of 967,600,821 is 1

Step 1: Since 967 > 600, we apply the division lemma to 967 and 600, to get

967 = 600 x 1 + 367

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 367 and 600, to get

600 = 367 x 1 + 233

Step 3: We consider the new divisor 367 and the new remainder 233, and apply the division lemma to get

367 = 233 x 1 + 134

We consider the new divisor 233 and the new remainder 134,and apply the division lemma to get

233 = 134 x 1 + 99

We consider the new divisor 134 and the new remainder 99,and apply the division lemma to get

134 = 99 x 1 + 35

We consider the new divisor 99 and the new remainder 35,and apply the division lemma to get

99 = 35 x 2 + 29

We consider the new divisor 35 and the new remainder 29,and apply the division lemma to get

35 = 29 x 1 + 6

We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get

29 = 6 x 4 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 967 and 600 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(35,29) = HCF(99,35) = HCF(134,99) = HCF(233,134) = HCF(367,233) = HCF(600,367) = HCF(967,600) .

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

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

821 = 1 x 821 + 0

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

Notice that 1 = HCF(821,1) .

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Frequently Asked Questions on HCF of 967, 600, 821 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 967, 600, 821?

Answer: HCF of 967, 600, 821 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 967, 600, 821 using Euclid's Algorithm?

Answer: For arbitrary numbers 967, 600, 821 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.