Highest Common Factor of 521, 689, 840 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 521, 689, 840 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 521, 689, 840 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 521, 689, 840 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 521, 689, 840 is 1.

HCF(521, 689, 840) = 1

HCF of 521, 689, 840 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 521, 689, 840 is 1.

Highest Common Factor of 521,689,840 using Euclid's algorithm

Highest Common Factor of 521,689,840 is 1

Step 1: Since 689 > 521, we apply the division lemma to 689 and 521, to get

689 = 521 x 1 + 168

Step 2: Since the reminder 521 ≠ 0, we apply division lemma to 168 and 521, to get

521 = 168 x 3 + 17

Step 3: We consider the new divisor 168 and the new remainder 17, and apply the division lemma to get

168 = 17 x 9 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 521 and 689 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(168,17) = HCF(521,168) = HCF(689,521) .

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

Step 1: Since 840 > 1, we apply the division lemma to 840 and 1, to get

840 = 1 x 840 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 840 is 1

Notice that 1 = HCF(840,1) .

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Frequently Asked Questions on HCF of 521, 689, 840 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 521, 689, 840?

Answer: HCF of 521, 689, 840 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 521, 689, 840 using Euclid's Algorithm?

Answer: For arbitrary numbers 521, 689, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.