Highest Common Factor of 687, 850, 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 687, 850, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 850, 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 687, 850, 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 687, 850, 174 is 1.

HCF(687, 850, 174) = 1

HCF of 687, 850, 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 687, 850, 174 is 1.

Highest Common Factor of 687,850,174 using Euclid's algorithm

Highest Common Factor of 687,850,174 is 1

Step 1: Since 850 > 687, we apply the division lemma to 850 and 687, to get

850 = 687 x 1 + 163

Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 163 and 687, to get

687 = 163 x 4 + 35

Step 3: We consider the new divisor 163 and the new remainder 35, and apply the division lemma to get

163 = 35 x 4 + 23

We consider the new divisor 35 and the new remainder 23,and apply the division lemma to get

35 = 23 x 1 + 12

We consider the new divisor 23 and the new remainder 12,and apply the division lemma to get

23 = 12 x 1 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 687 and 850 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(23,12) = HCF(35,23) = HCF(163,35) = HCF(687,163) = HCF(850,687) .

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 687, 850, 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 687, 850, 174?

Answer: HCF of 687, 850, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 850, 174 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 850, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.