Highest Common Factor of 7085, 1961 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 7085, 1961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7085, 1961 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 7085, 1961 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 7085, 1961 is 1.

HCF(7085, 1961) = 1

HCF of 7085, 1961 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 7085, 1961 is 1.

Highest Common Factor of 7085,1961 using Euclid's algorithm

Highest Common Factor of 7085,1961 is 1

Step 1: Since 7085 > 1961, we apply the division lemma to 7085 and 1961, to get

7085 = 1961 x 3 + 1202

Step 2: Since the reminder 1961 ≠ 0, we apply division lemma to 1202 and 1961, to get

1961 = 1202 x 1 + 759

Step 3: We consider the new divisor 1202 and the new remainder 759, and apply the division lemma to get

1202 = 759 x 1 + 443

We consider the new divisor 759 and the new remainder 443,and apply the division lemma to get

759 = 443 x 1 + 316

We consider the new divisor 443 and the new remainder 316,and apply the division lemma to get

443 = 316 x 1 + 127

We consider the new divisor 316 and the new remainder 127,and apply the division lemma to get

316 = 127 x 2 + 62

We consider the new divisor 127 and the new remainder 62,and apply the division lemma to get

127 = 62 x 2 + 3

We consider the new divisor 62 and the new remainder 3,and apply the division lemma to get

62 = 3 x 20 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 7085 and 1961 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(62,3) = HCF(127,62) = HCF(316,127) = HCF(443,316) = HCF(759,443) = HCF(1202,759) = HCF(1961,1202) = HCF(7085,1961) .

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Frequently Asked Questions on HCF of 7085, 1961 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 7085, 1961?

Answer: HCF of 7085, 1961 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7085, 1961 using Euclid's Algorithm?

Answer: For arbitrary numbers 7085, 1961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.