Highest Common Factor of 680, 446, 591 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 680, 446, 591 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 446, 591 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 680, 446, 591 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 680, 446, 591 is 1.

HCF(680, 446, 591) = 1

HCF of 680, 446, 591 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 680, 446, 591 is 1.

Highest Common Factor of 680,446,591 using Euclid's algorithm

Highest Common Factor of 680,446,591 is 1

Step 1: Since 680 > 446, we apply the division lemma to 680 and 446, to get

680 = 446 x 1 + 234

Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 234 and 446, to get

446 = 234 x 1 + 212

Step 3: We consider the new divisor 234 and the new remainder 212, and apply the division lemma to get

234 = 212 x 1 + 22

We consider the new divisor 212 and the new remainder 22,and apply the division lemma to get

212 = 22 x 9 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 680 and 446 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(212,22) = HCF(234,212) = HCF(446,234) = HCF(680,446) .

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

Step 1: Since 591 > 2, we apply the division lemma to 591 and 2, to get

591 = 2 x 295 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 591 is 1

Notice that 1 = HCF(2,1) = HCF(591,2) .

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Frequently Asked Questions on HCF of 680, 446, 591 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 680, 446, 591?

Answer: HCF of 680, 446, 591 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 446, 591 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 446, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.