Highest Common Factor of 467, 7732, 7154 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 467, 7732, 7154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 467, 7732, 7154 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 467, 7732, 7154 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 467, 7732, 7154 is 1.

HCF(467, 7732, 7154) = 1

HCF of 467, 7732, 7154 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 467, 7732, 7154 is 1.

Highest Common Factor of 467,7732,7154 using Euclid's algorithm

Highest Common Factor of 467,7732,7154 is 1

Step 1: Since 7732 > 467, we apply the division lemma to 7732 and 467, to get

7732 = 467 x 16 + 260

Step 2: Since the reminder 467 ≠ 0, we apply division lemma to 260 and 467, to get

467 = 260 x 1 + 207

Step 3: We consider the new divisor 260 and the new remainder 207, and apply the division lemma to get

260 = 207 x 1 + 53

We consider the new divisor 207 and the new remainder 53,and apply the division lemma to get

207 = 53 x 3 + 48

We consider the new divisor 53 and the new remainder 48,and apply the division lemma to get

53 = 48 x 1 + 5

We consider the new divisor 48 and the new remainder 5,and apply the division lemma to get

48 = 5 x 9 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 467 and 7732 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(48,5) = HCF(53,48) = HCF(207,53) = HCF(260,207) = HCF(467,260) = HCF(7732,467) .

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

Step 1: Since 7154 > 1, we apply the division lemma to 7154 and 1, to get

7154 = 1 x 7154 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7154 is 1

Notice that 1 = HCF(7154,1) .

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Frequently Asked Questions on HCF of 467, 7732, 7154 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 467, 7732, 7154?

Answer: HCF of 467, 7732, 7154 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 467, 7732, 7154 using Euclid's Algorithm?

Answer: For arbitrary numbers 467, 7732, 7154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.