Highest Common Factor of 605, 970, 351 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 605, 970, 351 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 605, 970, 351 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 605, 970, 351 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 605, 970, 351 is 1.

HCF(605, 970, 351) = 1

HCF of 605, 970, 351 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 605, 970, 351 is 1.

Highest Common Factor of 605,970,351 using Euclid's algorithm

Highest Common Factor of 605,970,351 is 1

Step 1: Since 970 > 605, we apply the division lemma to 970 and 605, to get

970 = 605 x 1 + 365

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 365 and 605, to get

605 = 365 x 1 + 240

Step 3: We consider the new divisor 365 and the new remainder 240, and apply the division lemma to get

365 = 240 x 1 + 125

We consider the new divisor 240 and the new remainder 125,and apply the division lemma to get

240 = 125 x 1 + 115

We consider the new divisor 125 and the new remainder 115,and apply the division lemma to get

125 = 115 x 1 + 10

We consider the new divisor 115 and the new remainder 10,and apply the division lemma to get

115 = 10 x 11 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 605 and 970 is 5

Notice that 5 = HCF(10,5) = HCF(115,10) = HCF(125,115) = HCF(240,125) = HCF(365,240) = HCF(605,365) = HCF(970,605) .

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

Step 1: Since 351 > 5, we apply the division lemma to 351 and 5, to get

351 = 5 x 70 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 351 is 1

Notice that 1 = HCF(5,1) = HCF(351,5) .

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Frequently Asked Questions on HCF of 605, 970, 351 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 605, 970, 351?

Answer: HCF of 605, 970, 351 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 605, 970, 351 using Euclid's Algorithm?

Answer: For arbitrary numbers 605, 970, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.