Highest Common Factor of 659, 885, 174 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 659, 885, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 659, 885, 174 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 659, 885, 174 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 659, 885, 174 is 1.

HCF(659, 885, 174) = 1

HCF of 659, 885, 174 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 659, 885, 174 is 1.

Highest Common Factor of 659,885,174 using Euclid's algorithm

Highest Common Factor of 659,885,174 is 1

Step 1: Since 885 > 659, we apply the division lemma to 885 and 659, to get

885 = 659 x 1 + 226

Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 226 and 659, to get

659 = 226 x 2 + 207

Step 3: We consider the new divisor 226 and the new remainder 207, and apply the division lemma to get

226 = 207 x 1 + 19

We consider the new divisor 207 and the new remainder 19,and apply the division lemma to get

207 = 19 x 10 + 17

We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get

19 = 17 x 1 + 2

We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get

17 = 2 x 8 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 659 and 885 is 1

Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(207,19) = HCF(226,207) = HCF(659,226) = HCF(885,659) .

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

Step 1: Since 174 > 1, we apply the division lemma to 174 and 1, to get

174 = 1 x 174 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 174 is 1

Notice that 1 = HCF(174,1) .

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Frequently Asked Questions on HCF of 659, 885, 174 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 659, 885, 174?

Answer: HCF of 659, 885, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 659, 885, 174 using Euclid's Algorithm?

Answer: For arbitrary numbers 659, 885, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.