Highest Common Factor of 3072, 8536, 10078 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 3072, 8536, 10078 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 3072, 8536, 10078 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 3072, 8536, 10078 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 3072, 8536, 10078 is 2.

HCF(3072, 8536, 10078) = 2

HCF of 3072, 8536, 10078 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 3072, 8536, 10078 is 2.

Highest Common Factor of 3072,8536,10078 using Euclid's algorithm

Highest Common Factor of 3072,8536,10078 is 2

Step 1: Since 8536 > 3072, we apply the division lemma to 8536 and 3072, to get

8536 = 3072 x 2 + 2392

Step 2: Since the reminder 3072 ≠ 0, we apply division lemma to 2392 and 3072, to get

3072 = 2392 x 1 + 680

Step 3: We consider the new divisor 2392 and the new remainder 680, and apply the division lemma to get

2392 = 680 x 3 + 352

We consider the new divisor 680 and the new remainder 352,and apply the division lemma to get

680 = 352 x 1 + 328

We consider the new divisor 352 and the new remainder 328,and apply the division lemma to get

352 = 328 x 1 + 24

We consider the new divisor 328 and the new remainder 24,and apply the division lemma to get

328 = 24 x 13 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 3072 and 8536 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(328,24) = HCF(352,328) = HCF(680,352) = HCF(2392,680) = HCF(3072,2392) = HCF(8536,3072) .

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

Step 1: Since 10078 > 8, we apply the division lemma to 10078 and 8, to get

10078 = 8 x 1259 + 6

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get

8 = 6 x 1 + 2

Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 10078 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(10078,8) .

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Frequently Asked Questions on HCF of 3072, 8536, 10078 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 3072, 8536, 10078?

Answer: HCF of 3072, 8536, 10078 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3072, 8536, 10078 using Euclid's Algorithm?

Answer: For arbitrary numbers 3072, 8536, 10078 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.