Highest Common Factor of 5678, 8976, 72026 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 5678, 8976, 72026 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5678, 8976, 72026 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 5678, 8976, 72026 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 5678, 8976, 72026 is 2.

HCF(5678, 8976, 72026) = 2

HCF of 5678, 8976, 72026 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 5678, 8976, 72026 is 2.

Highest Common Factor of 5678,8976,72026 using Euclid's algorithm

Highest Common Factor of 5678,8976,72026 is 2

Step 1: Since 8976 > 5678, we apply the division lemma to 8976 and 5678, to get

8976 = 5678 x 1 + 3298

Step 2: Since the reminder 5678 ≠ 0, we apply division lemma to 3298 and 5678, to get

5678 = 3298 x 1 + 2380

Step 3: We consider the new divisor 3298 and the new remainder 2380, and apply the division lemma to get

3298 = 2380 x 1 + 918

We consider the new divisor 2380 and the new remainder 918,and apply the division lemma to get

2380 = 918 x 2 + 544

We consider the new divisor 918 and the new remainder 544,and apply the division lemma to get

918 = 544 x 1 + 374

We consider the new divisor 544 and the new remainder 374,and apply the division lemma to get

544 = 374 x 1 + 170

We consider the new divisor 374 and the new remainder 170,and apply the division lemma to get

374 = 170 x 2 + 34

We consider the new divisor 170 and the new remainder 34,and apply the division lemma to get

170 = 34 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 5678 and 8976 is 34

Notice that 34 = HCF(170,34) = HCF(374,170) = HCF(544,374) = HCF(918,544) = HCF(2380,918) = HCF(3298,2380) = HCF(5678,3298) = HCF(8976,5678) .

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

Step 1: Since 72026 > 34, we apply the division lemma to 72026 and 34, to get

72026 = 34 x 2118 + 14

Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 14 and 34, to get

34 = 14 x 2 + 6

Step 3: We consider the new divisor 14 and the new remainder 6, and apply the division lemma to get

14 = 6 x 2 + 2

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 34 and 72026 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(72026,34) .

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Frequently Asked Questions on HCF of 5678, 8976, 72026 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 5678, 8976, 72026?

Answer: HCF of 5678, 8976, 72026 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5678, 8976, 72026 using Euclid's Algorithm?

Answer: For arbitrary numbers 5678, 8976, 72026 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.