Highest Common Factor of 304, 686, 755 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, 686, 755 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 304, 686, 755 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, 686, 755 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, 686, 755 is 1.

HCF(304, 686, 755) = 1

HCF of 304, 686, 755 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, 686, 755 is 1.

Highest Common Factor of 304,686,755 using Euclid's algorithm

Highest Common Factor of 304,686,755 is 1

Step 1: Since 686 > 304, we apply the division lemma to 686 and 304, to get

686 = 304 x 2 + 78

Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 78 and 304, to get

304 = 78 x 3 + 70

Step 3: We consider the new divisor 78 and the new remainder 70, and apply the division lemma to get

78 = 70 x 1 + 8

We consider the new divisor 70 and the new remainder 8,and apply the division lemma to get

70 = 8 x 8 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 304 and 686 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(70,8) = HCF(78,70) = HCF(304,78) = HCF(686,304) .

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

Step 1: Since 755 > 2, we apply the division lemma to 755 and 2, to get

755 = 2 x 377 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 755 is 1

Notice that 1 = HCF(2,1) = HCF(755,2) .

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Frequently Asked Questions on HCF of 304, 686, 755 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, 686, 755?

Answer: HCF of 304, 686, 755 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 304, 686, 755 using Euclid's Algorithm?

Answer: For arbitrary numbers 304, 686, 755 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.