Highest Common Factor of 605, 974, 729 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, 974, 729 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 605, 974, 729 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, 974, 729 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, 974, 729 is 1.

HCF(605, 974, 729) = 1

HCF of 605, 974, 729 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, 974, 729 is 1.

Highest Common Factor of 605,974,729 using Euclid's algorithm

Highest Common Factor of 605,974,729 is 1

Step 1: Since 974 > 605, we apply the division lemma to 974 and 605, to get

974 = 605 x 1 + 369

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 369 and 605, to get

605 = 369 x 1 + 236

Step 3: We consider the new divisor 369 and the new remainder 236, and apply the division lemma to get

369 = 236 x 1 + 133

We consider the new divisor 236 and the new remainder 133,and apply the division lemma to get

236 = 133 x 1 + 103

We consider the new divisor 133 and the new remainder 103,and apply the division lemma to get

133 = 103 x 1 + 30

We consider the new divisor 103 and the new remainder 30,and apply the division lemma to get

103 = 30 x 3 + 13

We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get

30 = 13 x 2 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 605 and 974 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(103,30) = HCF(133,103) = HCF(236,133) = HCF(369,236) = HCF(605,369) = HCF(974,605) .

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

Step 1: Since 729 > 1, we apply the division lemma to 729 and 1, to get

729 = 1 x 729 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 729 is 1

Notice that 1 = HCF(729,1) .

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Frequently Asked Questions on HCF of 605, 974, 729 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, 974, 729?

Answer: HCF of 605, 974, 729 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 605, 974, 729 using Euclid's Algorithm?

Answer: For arbitrary numbers 605, 974, 729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.