Highest Common Factor of 802, 3736, 6187 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, 3736, 6187 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 802, 3736, 6187 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 802, 3736, 6187 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, 3736, 6187 is 1.

HCF(802, 3736, 6187) = 1

HCF of 802, 3736, 6187 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, 3736, 6187 is 1.

Highest Common Factor of 802,3736,6187 using Euclid's algorithm

Highest Common Factor of 802,3736,6187 is 1

Step 1: Since 3736 > 802, we apply the division lemma to 3736 and 802, to get

3736 = 802 x 4 + 528

Step 2: Since the reminder 802 ≠ 0, we apply division lemma to 528 and 802, to get

802 = 528 x 1 + 274

Step 3: We consider the new divisor 528 and the new remainder 274, and apply the division lemma to get

528 = 274 x 1 + 254

We consider the new divisor 274 and the new remainder 254,and apply the division lemma to get

274 = 254 x 1 + 20

We consider the new divisor 254 and the new remainder 20,and apply the division lemma to get

254 = 20 x 12 + 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 3736 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(254,20) = HCF(274,254) = HCF(528,274) = HCF(802,528) = HCF(3736,802) .

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

Step 1: Since 6187 > 2, we apply the division lemma to 6187 and 2, to get

6187 = 2 x 3093 + 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 6187 is 1

Notice that 1 = HCF(2,1) = HCF(6187,2) .

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Frequently Asked Questions on HCF of 802, 3736, 6187 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, 3736, 6187?

Answer: HCF of 802, 3736, 6187 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 802, 3736, 6187 using Euclid's Algorithm?

Answer: For arbitrary numbers 802, 3736, 6187 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.