Highest Common Factor of 304, 476, 477 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 304, 476, 477 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 304, 476, 477 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 304, 476, 477 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 304, 476, 477 is 1.

HCF(304, 476, 477) = 1

HCF of 304, 476, 477 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 304, 476, 477 is 1.

Highest Common Factor of 304,476,477 using Euclid's algorithm

Highest Common Factor of 304,476,477 is 1

Step 1: Since 476 > 304, we apply the division lemma to 476 and 304, to get

476 = 304 x 1 + 172

Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 172 and 304, to get

304 = 172 x 1 + 132

Step 3: We consider the new divisor 172 and the new remainder 132, and apply the division lemma to get

172 = 132 x 1 + 40

We consider the new divisor 132 and the new remainder 40,and apply the division lemma to get

132 = 40 x 3 + 12

We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get

40 = 12 x 3 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 304 and 476 is 4

Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(132,40) = HCF(172,132) = HCF(304,172) = HCF(476,304) .

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

Step 1: Since 477 > 4, we apply the division lemma to 477 and 4, to get

477 = 4 x 119 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 477 is 1

Notice that 1 = HCF(4,1) = HCF(477,4) .

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Frequently Asked Questions on HCF of 304, 476, 477 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 304, 476, 477?

Answer: HCF of 304, 476, 477 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 304, 476, 477 using Euclid's Algorithm?

Answer: For arbitrary numbers 304, 476, 477 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.