Highest Common Factor of 802, 310, 302 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 802, 310, 302 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 802, 310, 302 is 2 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 802, 310, 302 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 802, 310, 302 is 2.

HCF(802, 310, 302) = 2

HCF of 802, 310, 302 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 802, 310, 302 is 2.

Highest Common Factor of 802,310,302 using Euclid's algorithm

Highest Common Factor of 802,310,302 is 2

Step 1: Since 802 > 310, we apply the division lemma to 802 and 310, to get

802 = 310 x 2 + 182

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 182 and 310, to get

310 = 182 x 1 + 128

Step 3: We consider the new divisor 182 and the new remainder 128, and apply the division lemma to get

182 = 128 x 1 + 54

We consider the new divisor 128 and the new remainder 54,and apply the division lemma to get

128 = 54 x 2 + 20

We consider the new divisor 54 and the new remainder 20,and apply the division lemma to get

54 = 20 x 2 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 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 802 and 310 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(54,20) = HCF(128,54) = HCF(182,128) = HCF(310,182) = HCF(802,310) .

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

Step 1: Since 302 > 2, we apply the division lemma to 302 and 2, to get

302 = 2 x 151 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 302 is 2

Notice that 2 = HCF(302,2) .

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Frequently Asked Questions on HCF of 802, 310, 302 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 802, 310, 302?

Answer: HCF of 802, 310, 302 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 802, 310, 302 using Euclid's Algorithm?

Answer: For arbitrary numbers 802, 310, 302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.