Highest Common Factor of 463, 865, 72 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, 865, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 463, 865, 72 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, 865, 72 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, 865, 72 is 1.

HCF(463, 865, 72) = 1

HCF of 463, 865, 72 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, 865, 72 is 1.

Highest Common Factor of 463,865,72 using Euclid's algorithm

Highest Common Factor of 463,865,72 is 1

Step 1: Since 865 > 463, we apply the division lemma to 865 and 463, to get

865 = 463 x 1 + 402

Step 2: Since the reminder 463 ≠ 0, we apply division lemma to 402 and 463, to get

463 = 402 x 1 + 61

Step 3: We consider the new divisor 402 and the new remainder 61, and apply the division lemma to get

402 = 61 x 6 + 36

We consider the new divisor 61 and the new remainder 36,and apply the division lemma to get

61 = 36 x 1 + 25

We consider the new divisor 36 and the new remainder 25,and apply the division lemma to get

36 = 25 x 1 + 11

We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get

25 = 11 x 2 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 463 and 865 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(36,25) = HCF(61,36) = HCF(402,61) = HCF(463,402) = HCF(865,463) .

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

Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get

72 = 1 x 72 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1

Notice that 1 = HCF(72,1) .

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Frequently Asked Questions on HCF of 463, 865, 72 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, 865, 72?

Answer: HCF of 463, 865, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 463, 865, 72 using Euclid's Algorithm?

Answer: For arbitrary numbers 463, 865, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.