Highest Common Factor of 685, 189, 472 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, 189, 472 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 685, 189, 472 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, 189, 472 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, 189, 472 is 1.

HCF(685, 189, 472) = 1

HCF of 685, 189, 472 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, 189, 472 is 1.

Highest Common Factor of 685,189,472 using Euclid's algorithm

Highest Common Factor of 685,189,472 is 1

Step 1: Since 685 > 189, we apply the division lemma to 685 and 189, to get

685 = 189 x 3 + 118

Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 118 and 189, to get

189 = 118 x 1 + 71

Step 3: We consider the new divisor 118 and the new remainder 71, and apply the division lemma to get

118 = 71 x 1 + 47

We consider the new divisor 71 and the new remainder 47,and apply the division lemma to get

71 = 47 x 1 + 24

We consider the new divisor 47 and the new remainder 24,and apply the division lemma to get

47 = 24 x 1 + 23

We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get

24 = 23 x 1 + 1

We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 685 and 189 is 1

Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(47,24) = HCF(71,47) = HCF(118,71) = HCF(189,118) = HCF(685,189) .

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

Step 1: Since 472 > 1, we apply the division lemma to 472 and 1, to get

472 = 1 x 472 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 472 is 1

Notice that 1 = HCF(472,1) .

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Frequently Asked Questions on HCF of 685, 189, 472 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, 189, 472?

Answer: HCF of 685, 189, 472 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 685, 189, 472 using Euclid's Algorithm?

Answer: For arbitrary numbers 685, 189, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.