Highest Common Factor of 7838, 9448, 56678 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 7838, 9448, 56678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 7838, 9448, 56678 is 2 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 7838, 9448, 56678 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 7838, 9448, 56678 is 2.

HCF(7838, 9448, 56678) = 2

HCF of 7838, 9448, 56678 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 7838, 9448, 56678 is 2.

Highest Common Factor of 7838,9448,56678 using Euclid's algorithm

Highest Common Factor of 7838,9448,56678 is 2

Step 1: Since 9448 > 7838, we apply the division lemma to 9448 and 7838, to get

9448 = 7838 x 1 + 1610

Step 2: Since the reminder 7838 ≠ 0, we apply division lemma to 1610 and 7838, to get

7838 = 1610 x 4 + 1398

Step 3: We consider the new divisor 1610 and the new remainder 1398, and apply the division lemma to get

1610 = 1398 x 1 + 212

We consider the new divisor 1398 and the new remainder 212,and apply the division lemma to get

1398 = 212 x 6 + 126

We consider the new divisor 212 and the new remainder 126,and apply the division lemma to get

212 = 126 x 1 + 86

We consider the new divisor 126 and the new remainder 86,and apply the division lemma to get

126 = 86 x 1 + 40

We consider the new divisor 86 and the new remainder 40,and apply the division lemma to get

86 = 40 x 2 + 6

We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get

40 = 6 x 6 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7838 and 9448 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(86,40) = HCF(126,86) = HCF(212,126) = HCF(1398,212) = HCF(1610,1398) = HCF(7838,1610) = HCF(9448,7838) .

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

Step 1: Since 56678 > 2, we apply the division lemma to 56678 and 2, to get

56678 = 2 x 28339 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 56678 is 2

Notice that 2 = HCF(56678,2) .

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Frequently Asked Questions on HCF of 7838, 9448, 56678 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 7838, 9448, 56678?

Answer: HCF of 7838, 9448, 56678 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7838, 9448, 56678 using Euclid's Algorithm?

Answer: For arbitrary numbers 7838, 9448, 56678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.