Highest Common Factor of 661, 934, 177 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, 934, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 661, 934, 177 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, 934, 177 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, 934, 177 is 1.

HCF(661, 934, 177) = 1

HCF of 661, 934, 177 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, 934, 177 is 1.

Highest Common Factor of 661,934,177 using Euclid's algorithm

Highest Common Factor of 661,934,177 is 1

Step 1: Since 934 > 661, we apply the division lemma to 934 and 661, to get

934 = 661 x 1 + 273

Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 273 and 661, to get

661 = 273 x 2 + 115

Step 3: We consider the new divisor 273 and the new remainder 115, and apply the division lemma to get

273 = 115 x 2 + 43

We consider the new divisor 115 and the new remainder 43,and apply the division lemma to get

115 = 43 x 2 + 29

We consider the new divisor 43 and the new remainder 29,and apply the division lemma to get

43 = 29 x 1 + 14

We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get

29 = 14 x 2 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 661 and 934 is 1

Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(43,29) = HCF(115,43) = HCF(273,115) = HCF(661,273) = HCF(934,661) .

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

Step 1: Since 177 > 1, we apply the division lemma to 177 and 1, to get

177 = 1 x 177 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 177 is 1

Notice that 1 = HCF(177,1) .

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Frequently Asked Questions on HCF of 661, 934, 177 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, 934, 177?

Answer: HCF of 661, 934, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 661, 934, 177 using Euclid's Algorithm?

Answer: For arbitrary numbers 661, 934, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.