Highest Common Factor of 7863, 1678 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 7863, 1678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7863, 1678 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 7863, 1678 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 7863, 1678 is 1.

HCF(7863, 1678) = 1

HCF of 7863, 1678 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 7863, 1678 is 1.

Highest Common Factor of 7863,1678 using Euclid's algorithm

Highest Common Factor of 7863,1678 is 1

Step 1: Since 7863 > 1678, we apply the division lemma to 7863 and 1678, to get

7863 = 1678 x 4 + 1151

Step 2: Since the reminder 1678 ≠ 0, we apply division lemma to 1151 and 1678, to get

1678 = 1151 x 1 + 527

Step 3: We consider the new divisor 1151 and the new remainder 527, and apply the division lemma to get

1151 = 527 x 2 + 97

We consider the new divisor 527 and the new remainder 97,and apply the division lemma to get

527 = 97 x 5 + 42

We consider the new divisor 97 and the new remainder 42,and apply the division lemma to get

97 = 42 x 2 + 13

We consider the new divisor 42 and the new remainder 13,and apply the division lemma to get

42 = 13 x 3 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7863 and 1678 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(42,13) = HCF(97,42) = HCF(527,97) = HCF(1151,527) = HCF(1678,1151) = HCF(7863,1678) .

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Frequently Asked Questions on HCF of 7863, 1678 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 7863, 1678?

Answer: HCF of 7863, 1678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7863, 1678 using Euclid's Algorithm?

Answer: For arbitrary numbers 7863, 1678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.