Highest Common Factor of 829, 348, 735 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 829, 348, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 829, 348, 735 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 829, 348, 735 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 829, 348, 735 is 1.

HCF(829, 348, 735) = 1

HCF of 829, 348, 735 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 829, 348, 735 is 1.

Highest Common Factor of 829,348,735 using Euclid's algorithm

Highest Common Factor of 829,348,735 is 1

Step 1: Since 829 > 348, we apply the division lemma to 829 and 348, to get

829 = 348 x 2 + 133

Step 2: Since the reminder 348 ≠ 0, we apply division lemma to 133 and 348, to get

348 = 133 x 2 + 82

Step 3: We consider the new divisor 133 and the new remainder 82, and apply the division lemma to get

133 = 82 x 1 + 51

We consider the new divisor 82 and the new remainder 51,and apply the division lemma to get

82 = 51 x 1 + 31

We consider the new divisor 51 and the new remainder 31,and apply the division lemma to get

51 = 31 x 1 + 20

We consider the new divisor 31 and the new remainder 20,and apply the division lemma to get

31 = 20 x 1 + 11

We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get

20 = 11 x 1 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 829 and 348 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(51,31) = HCF(82,51) = HCF(133,82) = HCF(348,133) = HCF(829,348) .

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

Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get

735 = 1 x 735 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1

Notice that 1 = HCF(735,1) .

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Frequently Asked Questions on HCF of 829, 348, 735 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 829, 348, 735?

Answer: HCF of 829, 348, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 829, 348, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 829, 348, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.