Highest Common Factor of 680, 761, 785 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 680, 761, 785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 680, 761, 785 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 680, 761, 785 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 680, 761, 785 is 1.

HCF(680, 761, 785) = 1

HCF of 680, 761, 785 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 680, 761, 785 is 1.

Highest Common Factor of 680,761,785 using Euclid's algorithm

Highest Common Factor of 680,761,785 is 1

Step 1: Since 761 > 680, we apply the division lemma to 761 and 680, to get

761 = 680 x 1 + 81

Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 81 and 680, to get

680 = 81 x 8 + 32

Step 3: We consider the new divisor 81 and the new remainder 32, and apply the division lemma to get

81 = 32 x 2 + 17

We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get

32 = 17 x 1 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 680 and 761 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(81,32) = HCF(680,81) = HCF(761,680) .

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

Step 1: Since 785 > 1, we apply the division lemma to 785 and 1, to get

785 = 1 x 785 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 785 is 1

Notice that 1 = HCF(785,1) .

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Frequently Asked Questions on HCF of 680, 761, 785 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 680, 761, 785?

Answer: HCF of 680, 761, 785 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 680, 761, 785 using Euclid's Algorithm?

Answer: For arbitrary numbers 680, 761, 785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.