Highest Common Factor of 759, 864, 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 759, 864, 694 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 759, 864, 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 759, 864, 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 759, 864, 694 is 1.

HCF(759, 864, 694) = 1

HCF of 759, 864, 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 759, 864, 694 is 1.

Highest Common Factor of 759,864,694 using Euclid's algorithm

Highest Common Factor of 759,864,694 is 1

Step 1: Since 864 > 759, we apply the division lemma to 864 and 759, to get

864 = 759 x 1 + 105

Step 2: Since the reminder 759 ≠ 0, we apply division lemma to 105 and 759, to get

759 = 105 x 7 + 24

Step 3: We consider the new divisor 105 and the new remainder 24, and apply the division lemma to get

105 = 24 x 4 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 759 and 864 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(105,24) = HCF(759,105) = HCF(864,759) .

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 759, 864, 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 759, 864, 694?

Answer: HCF of 759, 864, 694 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 759, 864, 694 using Euclid's Algorithm?

Answer: For arbitrary numbers 759, 864, 694 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.