Highest Common Factor of 729, 468, 170 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 729, 468, 170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 729, 468, 170 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 729, 468, 170 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 729, 468, 170 is 1.

HCF(729, 468, 170) = 1

HCF of 729, 468, 170 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 729, 468, 170 is 1.

Highest Common Factor of 729,468,170 using Euclid's algorithm

Highest Common Factor of 729,468,170 is 1

Step 1: Since 729 > 468, we apply the division lemma to 729 and 468, to get

729 = 468 x 1 + 261

Step 2: Since the reminder 468 ≠ 0, we apply division lemma to 261 and 468, to get

468 = 261 x 1 + 207

Step 3: We consider the new divisor 261 and the new remainder 207, and apply the division lemma to get

261 = 207 x 1 + 54

We consider the new divisor 207 and the new remainder 54,and apply the division lemma to get

207 = 54 x 3 + 45

We consider the new divisor 54 and the new remainder 45,and apply the division lemma to get

54 = 45 x 1 + 9

We consider the new divisor 45 and the new remainder 9,and apply the division lemma to get

45 = 9 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 729 and 468 is 9

Notice that 9 = HCF(45,9) = HCF(54,45) = HCF(207,54) = HCF(261,207) = HCF(468,261) = HCF(729,468) .

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

Step 1: Since 170 > 9, we apply the division lemma to 170 and 9, to get

170 = 9 x 18 + 8

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 8 and 9, to get

9 = 8 x 1 + 1

Step 3: We consider the new divisor 8 and the new remainder 1, and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 170 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(170,9) .

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Frequently Asked Questions on HCF of 729, 468, 170 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 729, 468, 170?

Answer: HCF of 729, 468, 170 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 729, 468, 170 using Euclid's Algorithm?

Answer: For arbitrary numbers 729, 468, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.