Highest Common Factor of 660, 931, 600 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, 931, 600 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 931, 600 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, 931, 600 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, 931, 600 is 1.

HCF(660, 931, 600) = 1

HCF of 660, 931, 600 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, 931, 600 is 1.

Highest Common Factor of 660,931,600 using Euclid's algorithm

Highest Common Factor of 660,931,600 is 1

Step 1: Since 931 > 660, we apply the division lemma to 931 and 660, to get

931 = 660 x 1 + 271

Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 271 and 660, to get

660 = 271 x 2 + 118

Step 3: We consider the new divisor 271 and the new remainder 118, and apply the division lemma to get

271 = 118 x 2 + 35

We consider the new divisor 118 and the new remainder 35,and apply the division lemma to get

118 = 35 x 3 + 13

We consider the new divisor 35 and the new remainder 13,and apply the division lemma to get

35 = 13 x 2 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 660 and 931 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(35,13) = HCF(118,35) = HCF(271,118) = HCF(660,271) = HCF(931,660) .

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

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

600 = 1 x 600 + 0

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

Notice that 1 = HCF(600,1) .

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Frequently Asked Questions on HCF of 660, 931, 600 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, 931, 600?

Answer: HCF of 660, 931, 600 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 931, 600 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 931, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.