Highest Common Factor of 977, 605, 134 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 977, 605, 134 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 977, 605, 134 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 977, 605, 134 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 977, 605, 134 is 1.

HCF(977, 605, 134) = 1

HCF of 977, 605, 134 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 977, 605, 134 is 1.

Highest Common Factor of 977,605,134 using Euclid's algorithm

Highest Common Factor of 977,605,134 is 1

Step 1: Since 977 > 605, we apply the division lemma to 977 and 605, to get

977 = 605 x 1 + 372

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 372 and 605, to get

605 = 372 x 1 + 233

Step 3: We consider the new divisor 372 and the new remainder 233, and apply the division lemma to get

372 = 233 x 1 + 139

We consider the new divisor 233 and the new remainder 139,and apply the division lemma to get

233 = 139 x 1 + 94

We consider the new divisor 139 and the new remainder 94,and apply the division lemma to get

139 = 94 x 1 + 45

We consider the new divisor 94 and the new remainder 45,and apply the division lemma to get

94 = 45 x 2 + 4

We consider the new divisor 45 and the new remainder 4,and apply the division lemma to get

45 = 4 x 11 + 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 977 and 605 is 1

Notice that 1 = HCF(4,1) = HCF(45,4) = HCF(94,45) = HCF(139,94) = HCF(233,139) = HCF(372,233) = HCF(605,372) = HCF(977,605) .

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

Step 1: Since 134 > 1, we apply the division lemma to 134 and 1, to get

134 = 1 x 134 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 134 is 1

Notice that 1 = HCF(134,1) .

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Frequently Asked Questions on HCF of 977, 605, 134 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 977, 605, 134?

Answer: HCF of 977, 605, 134 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 977, 605, 134 using Euclid's Algorithm?

Answer: For arbitrary numbers 977, 605, 134 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.