Highest Common Factor of 3478, 2488, 60661 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 3478, 2488, 60661 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3478, 2488, 60661 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 3478, 2488, 60661 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 3478, 2488, 60661 is 1.

HCF(3478, 2488, 60661) = 1

HCF of 3478, 2488, 60661 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 3478, 2488, 60661 is 1.

Highest Common Factor of 3478,2488,60661 using Euclid's algorithm

Highest Common Factor of 3478,2488,60661 is 1

Step 1: Since 3478 > 2488, we apply the division lemma to 3478 and 2488, to get

3478 = 2488 x 1 + 990

Step 2: Since the reminder 2488 ≠ 0, we apply division lemma to 990 and 2488, to get

2488 = 990 x 2 + 508

Step 3: We consider the new divisor 990 and the new remainder 508, and apply the division lemma to get

990 = 508 x 1 + 482

We consider the new divisor 508 and the new remainder 482,and apply the division lemma to get

508 = 482 x 1 + 26

We consider the new divisor 482 and the new remainder 26,and apply the division lemma to get

482 = 26 x 18 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3478 and 2488 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(482,26) = HCF(508,482) = HCF(990,508) = HCF(2488,990) = HCF(3478,2488) .

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

Step 1: Since 60661 > 2, we apply the division lemma to 60661 and 2, to get

60661 = 2 x 30330 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 60661 is 1

Notice that 1 = HCF(2,1) = HCF(60661,2) .

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Frequently Asked Questions on HCF of 3478, 2488, 60661 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 3478, 2488, 60661?

Answer: HCF of 3478, 2488, 60661 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3478, 2488, 60661 using Euclid's Algorithm?

Answer: For arbitrary numbers 3478, 2488, 60661 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.