Highest Common Factor of 610, 374, 93 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 610, 374, 93 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 610, 374, 93 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 610, 374, 93 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 610, 374, 93 is 1.

HCF(610, 374, 93) = 1

HCF of 610, 374, 93 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 610, 374, 93 is 1.

Highest Common Factor of 610,374,93 using Euclid's algorithm

Highest Common Factor of 610,374,93 is 1

Step 1: Since 610 > 374, we apply the division lemma to 610 and 374, to get

610 = 374 x 1 + 236

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 236 and 374, to get

374 = 236 x 1 + 138

Step 3: We consider the new divisor 236 and the new remainder 138, and apply the division lemma to get

236 = 138 x 1 + 98

We consider the new divisor 138 and the new remainder 98,and apply the division lemma to get

138 = 98 x 1 + 40

We consider the new divisor 98 and the new remainder 40,and apply the division lemma to get

98 = 40 x 2 + 18

We consider the new divisor 40 and the new remainder 18,and apply the division lemma to get

40 = 18 x 2 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 610 and 374 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(98,40) = HCF(138,98) = HCF(236,138) = HCF(374,236) = HCF(610,374) .

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

Step 1: Since 93 > 2, we apply the division lemma to 93 and 2, to get

93 = 2 x 46 + 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 93 is 1

Notice that 1 = HCF(2,1) = HCF(93,2) .

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Frequently Asked Questions on HCF of 610, 374, 93 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 610, 374, 93?

Answer: HCF of 610, 374, 93 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 610, 374, 93 using Euclid's Algorithm?

Answer: For arbitrary numbers 610, 374, 93 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.