Highest Common Factor of 502, 805, 409, 15 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 502, 805, 409, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 502, 805, 409, 15 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 502, 805, 409, 15 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 502, 805, 409, 15 is 1.

HCF(502, 805, 409, 15) = 1

HCF of 502, 805, 409, 15 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 502, 805, 409, 15 is 1.

Highest Common Factor of 502,805,409,15 using Euclid's algorithm

Highest Common Factor of 502,805,409,15 is 1

Step 1: Since 805 > 502, we apply the division lemma to 805 and 502, to get

805 = 502 x 1 + 303

Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 303 and 502, to get

502 = 303 x 1 + 199

Step 3: We consider the new divisor 303 and the new remainder 199, and apply the division lemma to get

303 = 199 x 1 + 104

We consider the new divisor 199 and the new remainder 104,and apply the division lemma to get

199 = 104 x 1 + 95

We consider the new divisor 104 and the new remainder 95,and apply the division lemma to get

104 = 95 x 1 + 9

We consider the new divisor 95 and the new remainder 9,and apply the division lemma to get

95 = 9 x 10 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 502 and 805 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(95,9) = HCF(104,95) = HCF(199,104) = HCF(303,199) = HCF(502,303) = HCF(805,502) .

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

Step 1: Since 409 > 1, we apply the division lemma to 409 and 1, to get

409 = 1 x 409 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 409 is 1

Notice that 1 = HCF(409,1) .

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

Step 1: Since 15 > 1, we apply the division lemma to 15 and 1, to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15 is 1

Notice that 1 = HCF(15,1) .

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Frequently Asked Questions on HCF of 502, 805, 409, 15 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 502, 805, 409, 15?

Answer: HCF of 502, 805, 409, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 502, 805, 409, 15 using Euclid's Algorithm?

Answer: For arbitrary numbers 502, 805, 409, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.