Highest Common Factor of 832, 663, 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 832, 663, 170 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 832, 663, 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 832, 663, 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 832, 663, 170 is 1.

HCF(832, 663, 170) = 1

HCF of 832, 663, 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 832, 663, 170 is 1.

Highest Common Factor of 832,663,170 using Euclid's algorithm

Highest Common Factor of 832,663,170 is 1

Step 1: Since 832 > 663, we apply the division lemma to 832 and 663, to get

832 = 663 x 1 + 169

Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 169 and 663, to get

663 = 169 x 3 + 156

Step 3: We consider the new divisor 169 and the new remainder 156, and apply the division lemma to get

169 = 156 x 1 + 13

We consider the new divisor 156 and the new remainder 13, and apply the division lemma to get

156 = 13 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 832 and 663 is 13

Notice that 13 = HCF(156,13) = HCF(169,156) = HCF(663,169) = HCF(832,663) .

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

Step 1: Since 170 > 13, we apply the division lemma to 170 and 13, to get

170 = 13 x 13 + 1

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 1 and 13, to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 170 is 1

Notice that 1 = HCF(13,1) = HCF(170,13) .

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Frequently Asked Questions on HCF of 832, 663, 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 832, 663, 170?

Answer: HCF of 832, 663, 170 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 832, 663, 170 using Euclid's Algorithm?

Answer: For arbitrary numbers 832, 663, 170 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.