Highest Common Factor of 821, 929, 349 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 821, 929, 349 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 821, 929, 349 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 821, 929, 349 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 821, 929, 349 is 1.

HCF(821, 929, 349) = 1

HCF of 821, 929, 349 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 821, 929, 349 is 1.

Highest Common Factor of 821,929,349 using Euclid's algorithm

Highest Common Factor of 821,929,349 is 1

Step 1: Since 929 > 821, we apply the division lemma to 929 and 821, to get

929 = 821 x 1 + 108

Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 108 and 821, to get

821 = 108 x 7 + 65

Step 3: We consider the new divisor 108 and the new remainder 65, and apply the division lemma to get

108 = 65 x 1 + 43

We consider the new divisor 65 and the new remainder 43,and apply the division lemma to get

65 = 43 x 1 + 22

We consider the new divisor 43 and the new remainder 22,and apply the division lemma to get

43 = 22 x 1 + 21

We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get

22 = 21 x 1 + 1

We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 929 is 1

Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(43,22) = HCF(65,43) = HCF(108,65) = HCF(821,108) = HCF(929,821) .

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

Step 1: Since 349 > 1, we apply the division lemma to 349 and 1, to get

349 = 1 x 349 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 349 is 1

Notice that 1 = HCF(349,1) .

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Frequently Asked Questions on HCF of 821, 929, 349 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 821, 929, 349?

Answer: HCF of 821, 929, 349 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 821, 929, 349 using Euclid's Algorithm?

Answer: For arbitrary numbers 821, 929, 349 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.