Highest Common Factor of 685, 440, 173 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 685, 440, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 440, 173 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 685, 440, 173 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 685, 440, 173 is 1.

HCF(685, 440, 173) = 1

HCF of 685, 440, 173 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 685, 440, 173 is 1.

Highest Common Factor of 685,440,173 using Euclid's algorithm

Highest Common Factor of 685,440,173 is 1

Step 1: Since 685 > 440, we apply the division lemma to 685 and 440, to get

685 = 440 x 1 + 245

Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 245 and 440, to get

440 = 245 x 1 + 195

Step 3: We consider the new divisor 245 and the new remainder 195, and apply the division lemma to get

245 = 195 x 1 + 50

We consider the new divisor 195 and the new remainder 50,and apply the division lemma to get

195 = 50 x 3 + 45

We consider the new divisor 50 and the new remainder 45,and apply the division lemma to get

50 = 45 x 1 + 5

We consider the new divisor 45 and the new remainder 5,and apply the division lemma to get

45 = 5 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 685 and 440 is 5

Notice that 5 = HCF(45,5) = HCF(50,45) = HCF(195,50) = HCF(245,195) = HCF(440,245) = HCF(685,440) .

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

Step 1: Since 173 > 5, we apply the division lemma to 173 and 5, to get

173 = 5 x 34 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 5 and 173 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(173,5) .

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Frequently Asked Questions on HCF of 685, 440, 173 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 685, 440, 173?

Answer: HCF of 685, 440, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 440, 173 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 440, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.