Highest Common Factor of 3145, 8602 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 3145, 8602 i.e. 17 the largest integer that leaves a remainder zero for all numbers.

HCF of 3145, 8602 is 17 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 3145, 8602 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 3145, 8602 is 17.

HCF(3145, 8602) = 17

HCF of 3145, 8602 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 3145, 8602 is 17.

Highest Common Factor of 3145,8602 using Euclid's algorithm

Highest Common Factor of 3145,8602 is 17

Step 1: Since 8602 > 3145, we apply the division lemma to 8602 and 3145, to get

8602 = 3145 x 2 + 2312

Step 2: Since the reminder 3145 ≠ 0, we apply division lemma to 2312 and 3145, to get

3145 = 2312 x 1 + 833

Step 3: We consider the new divisor 2312 and the new remainder 833, and apply the division lemma to get

2312 = 833 x 2 + 646

We consider the new divisor 833 and the new remainder 646,and apply the division lemma to get

833 = 646 x 1 + 187

We consider the new divisor 646 and the new remainder 187,and apply the division lemma to get

646 = 187 x 3 + 85

We consider the new divisor 187 and the new remainder 85,and apply the division lemma to get

187 = 85 x 2 + 17

We consider the new divisor 85 and the new remainder 17,and apply the division lemma to get

85 = 17 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 3145 and 8602 is 17

Notice that 17 = HCF(85,17) = HCF(187,85) = HCF(646,187) = HCF(833,646) = HCF(2312,833) = HCF(3145,2312) = HCF(8602,3145) .

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Frequently Asked Questions on HCF of 3145, 8602 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 3145, 8602?

Answer: HCF of 3145, 8602 is 17 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3145, 8602 using Euclid's Algorithm?

Answer: For arbitrary numbers 3145, 8602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.