Highest Common Factor of 303, 516, 698, 71 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 303, 516, 698, 71 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 303, 516, 698, 71 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 303, 516, 698, 71 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 303, 516, 698, 71 is 1.

HCF(303, 516, 698, 71) = 1

HCF of 303, 516, 698, 71 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 303, 516, 698, 71 is 1.

Highest Common Factor of 303,516,698,71 using Euclid's algorithm

Highest Common Factor of 303,516,698,71 is 1

Step 1: Since 516 > 303, we apply the division lemma to 516 and 303, to get

516 = 303 x 1 + 213

Step 2: Since the reminder 303 ≠ 0, we apply division lemma to 213 and 303, to get

303 = 213 x 1 + 90

Step 3: We consider the new divisor 213 and the new remainder 90, and apply the division lemma to get

213 = 90 x 2 + 33

We consider the new divisor 90 and the new remainder 33,and apply the division lemma to get

90 = 33 x 2 + 24

We consider the new divisor 33 and the new remainder 24,and apply the division lemma to get

33 = 24 x 1 + 9

We consider the new divisor 24 and the new remainder 9,and apply the division lemma to get

24 = 9 x 2 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 303 and 516 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(33,24) = HCF(90,33) = HCF(213,90) = HCF(303,213) = HCF(516,303) .

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

Step 1: Since 698 > 3, we apply the division lemma to 698 and 3, to get

698 = 3 x 232 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 698 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(698,3) .

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

Step 1: Since 71 > 1, we apply the division lemma to 71 and 1, to get

71 = 1 x 71 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 71 is 1

Notice that 1 = HCF(71,1) .

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Frequently Asked Questions on HCF of 303, 516, 698, 71 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 303, 516, 698, 71?

Answer: HCF of 303, 516, 698, 71 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 303, 516, 698, 71 using Euclid's Algorithm?

Answer: For arbitrary numbers 303, 516, 698, 71 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.