Highest Common Factor of 502, 685, 378 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 502, 685, 378 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 502, 685, 378 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 502, 685, 378 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 502, 685, 378 is 1.

HCF(502, 685, 378) = 1

HCF of 502, 685, 378 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 502, 685, 378 is 1.

Highest Common Factor of 502,685,378 using Euclid's algorithm

Highest Common Factor of 502,685,378 is 1

Step 1: Since 685 > 502, we apply the division lemma to 685 and 502, to get

685 = 502 x 1 + 183

Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 183 and 502, to get

502 = 183 x 2 + 136

Step 3: We consider the new divisor 183 and the new remainder 136, and apply the division lemma to get

183 = 136 x 1 + 47

We consider the new divisor 136 and the new remainder 47,and apply the division lemma to get

136 = 47 x 2 + 42

We consider the new divisor 47 and the new remainder 42,and apply the division lemma to get

47 = 42 x 1 + 5

We consider the new divisor 42 and the new remainder 5,and apply the division lemma to get

42 = 5 x 8 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 502 and 685 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) = HCF(47,42) = HCF(136,47) = HCF(183,136) = HCF(502,183) = HCF(685,502) .

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

Step 1: Since 378 > 1, we apply the division lemma to 378 and 1, to get

378 = 1 x 378 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 378 is 1

Notice that 1 = HCF(378,1) .

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Frequently Asked Questions on HCF of 502, 685, 378 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 502, 685, 378?

Answer: HCF of 502, 685, 378 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 502, 685, 378 using Euclid's Algorithm?

Answer: For arbitrary numbers 502, 685, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.