Highest Common Factor of 460, 693, 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 460, 693, 170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 460, 693, 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 460, 693, 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 460, 693, 170 is 1.

HCF(460, 693, 170) = 1

HCF of 460, 693, 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 460, 693, 170 is 1.

Highest Common Factor of 460,693,170 using Euclid's algorithm

Highest Common Factor of 460,693,170 is 1

Step 1: Since 693 > 460, we apply the division lemma to 693 and 460, to get

693 = 460 x 1 + 233

Step 2: Since the reminder 460 ≠ 0, we apply division lemma to 233 and 460, to get

460 = 233 x 1 + 227

Step 3: We consider the new divisor 233 and the new remainder 227, and apply the division lemma to get

233 = 227 x 1 + 6

We consider the new divisor 227 and the new remainder 6,and apply the division lemma to get

227 = 6 x 37 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma 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 460 and 693 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(227,6) = HCF(233,227) = HCF(460,233) = HCF(693,460) .

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

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

170 = 1 x 170 + 0

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

Notice that 1 = HCF(170,1) .

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Frequently Asked Questions on HCF of 460, 693, 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 460, 693, 170?

Answer: HCF of 460, 693, 170 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 460, 693, 170 using Euclid's Algorithm?

Answer: For arbitrary numbers 460, 693, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.