Highest Common Factor of 754, 467 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 754, 467 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 754, 467 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 754, 467 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 754, 467 is 1.

HCF(754, 467) = 1

HCF of 754, 467 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 754, 467 is 1.

Highest Common Factor of 754,467 using Euclid's algorithm

Highest Common Factor of 754,467 is 1

Step 1: Since 754 > 467, we apply the division lemma to 754 and 467, to get

754 = 467 x 1 + 287

Step 2: Since the reminder 467 ≠ 0, we apply division lemma to 287 and 467, to get

467 = 287 x 1 + 180

Step 3: We consider the new divisor 287 and the new remainder 180, and apply the division lemma to get

287 = 180 x 1 + 107

We consider the new divisor 180 and the new remainder 107,and apply the division lemma to get

180 = 107 x 1 + 73

We consider the new divisor 107 and the new remainder 73,and apply the division lemma to get

107 = 73 x 1 + 34

We consider the new divisor 73 and the new remainder 34,and apply the division lemma to get

73 = 34 x 2 + 5

We consider the new divisor 34 and the new remainder 5,and apply the division lemma to get

34 = 5 x 6 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 754 and 467 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(34,5) = HCF(73,34) = HCF(107,73) = HCF(180,107) = HCF(287,180) = HCF(467,287) = HCF(754,467) .

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Frequently Asked Questions on HCF of 754, 467 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 754, 467?

Answer: HCF of 754, 467 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 754, 467 using Euclid's Algorithm?

Answer: For arbitrary numbers 754, 467 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.