Highest Common Factor of 977, 765, 599 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, 765, 599 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 977, 765, 599 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, 765, 599 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, 765, 599 is 1.

HCF(977, 765, 599) = 1

HCF of 977, 765, 599 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, 765, 599 is 1.

Highest Common Factor of 977,765,599 using Euclid's algorithm

Highest Common Factor of 977,765,599 is 1

Step 1: Since 977 > 765, we apply the division lemma to 977 and 765, to get

977 = 765 x 1 + 212

Step 2: Since the reminder 765 ≠ 0, we apply division lemma to 212 and 765, to get

765 = 212 x 3 + 129

Step 3: We consider the new divisor 212 and the new remainder 129, and apply the division lemma to get

212 = 129 x 1 + 83

We consider the new divisor 129 and the new remainder 83,and apply the division lemma to get

129 = 83 x 1 + 46

We consider the new divisor 83 and the new remainder 46,and apply the division lemma to get

83 = 46 x 1 + 37

We consider the new divisor 46 and the new remainder 37,and apply the division lemma to get

46 = 37 x 1 + 9

We consider the new divisor 37 and the new remainder 9,and apply the division lemma to get

37 = 9 x 4 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 765 is 1

Notice that 1 = HCF(9,1) = HCF(37,9) = HCF(46,37) = HCF(83,46) = HCF(129,83) = HCF(212,129) = HCF(765,212) = HCF(977,765) .

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

Step 1: Since 599 > 1, we apply the division lemma to 599 and 1, to get

599 = 1 x 599 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 599 is 1

Notice that 1 = HCF(599,1) .

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Frequently Asked Questions on HCF of 977, 765, 599 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, 765, 599?

Answer: HCF of 977, 765, 599 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 977, 765, 599 using Euclid's Algorithm?

Answer: For arbitrary numbers 977, 765, 599 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.