Highest Common Factor of 8002, 577 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 8002, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8002, 577 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 8002, 577 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 8002, 577 is 1.

HCF(8002, 577) = 1

HCF of 8002, 577 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 8002, 577 is 1.

Highest Common Factor of 8002,577 using Euclid's algorithm

Highest Common Factor of 8002,577 is 1

Step 1: Since 8002 > 577, we apply the division lemma to 8002 and 577, to get

8002 = 577 x 13 + 501

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 501 and 577, to get

577 = 501 x 1 + 76

Step 3: We consider the new divisor 501 and the new remainder 76, and apply the division lemma to get

501 = 76 x 6 + 45

We consider the new divisor 76 and the new remainder 45,and apply the division lemma to get

76 = 45 x 1 + 31

We consider the new divisor 45 and the new remainder 31,and apply the division lemma to get

45 = 31 x 1 + 14

We consider the new divisor 31 and the new remainder 14,and apply the division lemma to get

31 = 14 x 2 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 8002 and 577 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(31,14) = HCF(45,31) = HCF(76,45) = HCF(501,76) = HCF(577,501) = HCF(8002,577) .

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Frequently Asked Questions on HCF of 8002, 577 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 8002, 577?

Answer: HCF of 8002, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8002, 577 using Euclid's Algorithm?

Answer: For arbitrary numbers 8002, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.