Highest Common Factor of 520, 299, 802 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 520, 299, 802 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 520, 299, 802 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 520, 299, 802 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 520, 299, 802 is 1.

HCF(520, 299, 802) = 1

HCF of 520, 299, 802 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 520, 299, 802 is 1.

Highest Common Factor of 520,299,802 using Euclid's algorithm

Highest Common Factor of 520,299,802 is 1

Step 1: Since 520 > 299, we apply the division lemma to 520 and 299, to get

520 = 299 x 1 + 221

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 221 and 299, to get

299 = 221 x 1 + 78

Step 3: We consider the new divisor 221 and the new remainder 78, and apply the division lemma to get

221 = 78 x 2 + 65

We consider the new divisor 78 and the new remainder 65,and apply the division lemma to get

78 = 65 x 1 + 13

We consider the new divisor 65 and the new remainder 13,and apply the division lemma to get

65 = 13 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 520 and 299 is 13

Notice that 13 = HCF(65,13) = HCF(78,65) = HCF(221,78) = HCF(299,221) = HCF(520,299) .

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

Step 1: Since 802 > 13, we apply the division lemma to 802 and 13, to get

802 = 13 x 61 + 9

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 9 and 13, to get

13 = 9 x 1 + 4

Step 3: We consider the new divisor 9 and the new remainder 4, and apply the division lemma to get

9 = 4 x 2 + 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 13 and 802 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(802,13) .

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Frequently Asked Questions on HCF of 520, 299, 802 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 520, 299, 802?

Answer: HCF of 520, 299, 802 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 520, 299, 802 using Euclid's Algorithm?

Answer: For arbitrary numbers 520, 299, 802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.