Highest Common Factor of 463, 729, 34 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 463, 729, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 463, 729, 34 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 463, 729, 34 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 463, 729, 34 is 1.

HCF(463, 729, 34) = 1

HCF of 463, 729, 34 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 463, 729, 34 is 1.

Highest Common Factor of 463,729,34 using Euclid's algorithm

Highest Common Factor of 463,729,34 is 1

Step 1: Since 729 > 463, we apply the division lemma to 729 and 463, to get

729 = 463 x 1 + 266

Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 266 and 463, to get

463 = 266 x 1 + 197

Step 3: We consider the new divisor 266 and the new remainder 197, and apply the division lemma to get

266 = 197 x 1 + 69

We consider the new divisor 197 and the new remainder 69,and apply the division lemma to get

197 = 69 x 2 + 59

We consider the new divisor 69 and the new remainder 59,and apply the division lemma to get

69 = 59 x 1 + 10

We consider the new divisor 59 and the new remainder 10,and apply the division lemma to get

59 = 10 x 5 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 463 and 729 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(59,10) = HCF(69,59) = HCF(197,69) = HCF(266,197) = HCF(463,266) = HCF(729,463) .

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

Step 1: Since 34 > 1, we apply the division lemma to 34 and 1, to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34 is 1

Notice that 1 = HCF(34,1) .

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Frequently Asked Questions on HCF of 463, 729, 34 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 463, 729, 34?

Answer: HCF of 463, 729, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 463, 729, 34 using Euclid's Algorithm?

Answer: For arbitrary numbers 463, 729, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.