Highest Common Factor of 661, 937, 612 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 661, 937, 612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 661, 937, 612 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 661, 937, 612 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 661, 937, 612 is 1.

HCF(661, 937, 612) = 1

HCF of 661, 937, 612 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 661, 937, 612 is 1.

Highest Common Factor of 661,937,612 using Euclid's algorithm

Highest Common Factor of 661,937,612 is 1

Step 1: Since 937 > 661, we apply the division lemma to 937 and 661, to get

937 = 661 x 1 + 276

Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 276 and 661, to get

661 = 276 x 2 + 109

Step 3: We consider the new divisor 276 and the new remainder 109, and apply the division lemma to get

276 = 109 x 2 + 58

We consider the new divisor 109 and the new remainder 58,and apply the division lemma to get

109 = 58 x 1 + 51

We consider the new divisor 58 and the new remainder 51,and apply the division lemma to get

58 = 51 x 1 + 7

We consider the new divisor 51 and the new remainder 7,and apply the division lemma to get

51 = 7 x 7 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 661 and 937 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(51,7) = HCF(58,51) = HCF(109,58) = HCF(276,109) = HCF(661,276) = HCF(937,661) .

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

Step 1: Since 612 > 1, we apply the division lemma to 612 and 1, to get

612 = 1 x 612 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 612 is 1

Notice that 1 = HCF(612,1) .

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Frequently Asked Questions on HCF of 661, 937, 612 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 661, 937, 612?

Answer: HCF of 661, 937, 612 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 661, 937, 612 using Euclid's Algorithm?

Answer: For arbitrary numbers 661, 937, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.