Highest Common Factor of 678, 530, 303 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 678, 530, 303 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 678, 530, 303 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 678, 530, 303 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 678, 530, 303 is 1.

HCF(678, 530, 303) = 1

HCF of 678, 530, 303 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 678, 530, 303 is 1.

Highest Common Factor of 678,530,303 using Euclid's algorithm

Highest Common Factor of 678,530,303 is 1

Step 1: Since 678 > 530, we apply the division lemma to 678 and 530, to get

678 = 530 x 1 + 148

Step 2: Since the reminder 530 ≠ 0, we apply division lemma to 148 and 530, to get

530 = 148 x 3 + 86

Step 3: We consider the new divisor 148 and the new remainder 86, and apply the division lemma to get

148 = 86 x 1 + 62

We consider the new divisor 86 and the new remainder 62,and apply the division lemma to get

86 = 62 x 1 + 24

We consider the new divisor 62 and the new remainder 24,and apply the division lemma to get

62 = 24 x 2 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 530 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(62,24) = HCF(86,62) = HCF(148,86) = HCF(530,148) = HCF(678,530) .

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

Step 1: Since 303 > 2, we apply the division lemma to 303 and 2, to get

303 = 2 x 151 + 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 303 is 1

Notice that 1 = HCF(2,1) = HCF(303,2) .

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Frequently Asked Questions on HCF of 678, 530, 303 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 678, 530, 303?

Answer: HCF of 678, 530, 303 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 678, 530, 303 using Euclid's Algorithm?

Answer: For arbitrary numbers 678, 530, 303 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.