Highest Common Factor of 703, 77912 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 703, 77912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 703, 77912 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 703, 77912 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 703, 77912 is 1.

HCF(703, 77912) = 1

HCF of 703, 77912 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 703, 77912 is 1.

Highest Common Factor of 703,77912 using Euclid's algorithm

Highest Common Factor of 703,77912 is 1

Step 1: Since 77912 > 703, we apply the division lemma to 77912 and 703, to get

77912 = 703 x 110 + 582

Step 2: Since the reminder 703 ≠ 0, we apply division lemma to 582 and 703, to get

703 = 582 x 1 + 121

Step 3: We consider the new divisor 582 and the new remainder 121, and apply the division lemma to get

582 = 121 x 4 + 98

We consider the new divisor 121 and the new remainder 98,and apply the division lemma to get

121 = 98 x 1 + 23

We consider the new divisor 98 and the new remainder 23,and apply the division lemma to get

98 = 23 x 4 + 6

We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get

23 = 6 x 3 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 703 and 77912 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(98,23) = HCF(121,98) = HCF(582,121) = HCF(703,582) = HCF(77912,703) .

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Frequently Asked Questions on HCF of 703, 77912 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 703, 77912?

Answer: HCF of 703, 77912 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 703, 77912 using Euclid's Algorithm?

Answer: For arbitrary numbers 703, 77912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.