Highest Common Factor of 7231, 8546, 78104 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 7231, 8546, 78104 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7231, 8546, 78104 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 7231, 8546, 78104 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 7231, 8546, 78104 is 1.

HCF(7231, 8546, 78104) = 1

HCF of 7231, 8546, 78104 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 7231, 8546, 78104 is 1.

Highest Common Factor of 7231,8546,78104 using Euclid's algorithm

Highest Common Factor of 7231,8546,78104 is 1

Step 1: Since 8546 > 7231, we apply the division lemma to 8546 and 7231, to get

8546 = 7231 x 1 + 1315

Step 2: Since the reminder 7231 ≠ 0, we apply division lemma to 1315 and 7231, to get

7231 = 1315 x 5 + 656

Step 3: We consider the new divisor 1315 and the new remainder 656, and apply the division lemma to get

1315 = 656 x 2 + 3

We consider the new divisor 656 and the new remainder 3,and apply the division lemma to get

656 = 3 x 218 + 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 7231 and 8546 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(656,3) = HCF(1315,656) = HCF(7231,1315) = HCF(8546,7231) .

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

Step 1: Since 78104 > 1, we apply the division lemma to 78104 and 1, to get

78104 = 1 x 78104 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78104 is 1

Notice that 1 = HCF(78104,1) .

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Frequently Asked Questions on HCF of 7231, 8546, 78104 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 7231, 8546, 78104?

Answer: HCF of 7231, 8546, 78104 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7231, 8546, 78104 using Euclid's Algorithm?

Answer: For arbitrary numbers 7231, 8546, 78104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.