Highest Common Factor of 660, 391, 830 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 660, 391, 830 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 391, 830 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 660, 391, 830 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 660, 391, 830 is 1.

HCF(660, 391, 830) = 1

HCF of 660, 391, 830 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 660, 391, 830 is 1.

Highest Common Factor of 660,391,830 using Euclid's algorithm

Highest Common Factor of 660,391,830 is 1

Step 1: Since 660 > 391, we apply the division lemma to 660 and 391, to get

660 = 391 x 1 + 269

Step 2: Since the reminder 391 ≠ 0, we apply division lemma to 269 and 391, to get

391 = 269 x 1 + 122

Step 3: We consider the new divisor 269 and the new remainder 122, and apply the division lemma to get

269 = 122 x 2 + 25

We consider the new divisor 122 and the new remainder 25,and apply the division lemma to get

122 = 25 x 4 + 22

We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get

25 = 22 x 1 + 3

We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get

22 = 3 x 7 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 660 and 391 is 1

Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(122,25) = HCF(269,122) = HCF(391,269) = HCF(660,391) .

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

Step 1: Since 830 > 1, we apply the division lemma to 830 and 1, to get

830 = 1 x 830 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 830 is 1

Notice that 1 = HCF(830,1) .

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Frequently Asked Questions on HCF of 660, 391, 830 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 660, 391, 830?

Answer: HCF of 660, 391, 830 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 391, 830 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 391, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.