Highest Common Factor of 207, 285, 694 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 207, 285, 694 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 207, 285, 694 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 207, 285, 694 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 207, 285, 694 is 1.

HCF(207, 285, 694) = 1

HCF of 207, 285, 694 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 207, 285, 694 is 1.

Highest Common Factor of 207,285,694 using Euclid's algorithm

Highest Common Factor of 207,285,694 is 1

Step 1: Since 285 > 207, we apply the division lemma to 285 and 207, to get

285 = 207 x 1 + 78

Step 2: Since the reminder 207 ≠ 0, we apply division lemma to 78 and 207, to get

207 = 78 x 2 + 51

Step 3: We consider the new divisor 78 and the new remainder 51, and apply the division lemma to get

78 = 51 x 1 + 27

We consider the new divisor 51 and the new remainder 27,and apply the division lemma to get

51 = 27 x 1 + 24

We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get

27 = 24 x 1 + 3

We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get

24 = 3 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 207 and 285 is 3

Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(51,27) = HCF(78,51) = HCF(207,78) = HCF(285,207) .

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

Step 1: Since 694 > 3, we apply the division lemma to 694 and 3, to get

694 = 3 x 231 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 694 is 1

Notice that 1 = HCF(3,1) = HCF(694,3) .

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Frequently Asked Questions on HCF of 207, 285, 694 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 207, 285, 694?

Answer: HCF of 207, 285, 694 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 207, 285, 694 using Euclid's Algorithm?

Answer: For arbitrary numbers 207, 285, 694 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.