Highest Common Factor of 1415, 7582 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 1415, 7582 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1415, 7582 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 1415, 7582 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 1415, 7582 is 1.

HCF(1415, 7582) = 1

HCF of 1415, 7582 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 1415, 7582 is 1.

Highest Common Factor of 1415,7582 using Euclid's algorithm

Highest Common Factor of 1415,7582 is 1

Step 1: Since 7582 > 1415, we apply the division lemma to 7582 and 1415, to get

7582 = 1415 x 5 + 507

Step 2: Since the reminder 1415 ≠ 0, we apply division lemma to 507 and 1415, to get

1415 = 507 x 2 + 401

Step 3: We consider the new divisor 507 and the new remainder 401, and apply the division lemma to get

507 = 401 x 1 + 106

We consider the new divisor 401 and the new remainder 106,and apply the division lemma to get

401 = 106 x 3 + 83

We consider the new divisor 106 and the new remainder 83,and apply the division lemma to get

106 = 83 x 1 + 23

We consider the new divisor 83 and the new remainder 23,and apply the division lemma to get

83 = 23 x 3 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 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 1415 and 7582 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(83,23) = HCF(106,83) = HCF(401,106) = HCF(507,401) = HCF(1415,507) = HCF(7582,1415) .

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Frequently Asked Questions on HCF of 1415, 7582 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 1415, 7582?

Answer: HCF of 1415, 7582 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1415, 7582 using Euclid's Algorithm?

Answer: For arbitrary numbers 1415, 7582 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.