Highest Common Factor of 8145, 1669, 42060 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 8145, 1669, 42060 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8145, 1669, 42060 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 8145, 1669, 42060 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 8145, 1669, 42060 is 1.

HCF(8145, 1669, 42060) = 1

HCF of 8145, 1669, 42060 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 8145, 1669, 42060 is 1.

Highest Common Factor of 8145,1669,42060 using Euclid's algorithm

Highest Common Factor of 8145,1669,42060 is 1

Step 1: Since 8145 > 1669, we apply the division lemma to 8145 and 1669, to get

8145 = 1669 x 4 + 1469

Step 2: Since the reminder 1669 ≠ 0, we apply division lemma to 1469 and 1669, to get

1669 = 1469 x 1 + 200

Step 3: We consider the new divisor 1469 and the new remainder 200, and apply the division lemma to get

1469 = 200 x 7 + 69

We consider the new divisor 200 and the new remainder 69,and apply the division lemma to get

200 = 69 x 2 + 62

We consider the new divisor 69 and the new remainder 62,and apply the division lemma to get

69 = 62 x 1 + 7

We consider the new divisor 62 and the new remainder 7,and apply the division lemma to get

62 = 7 x 8 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8145 and 1669 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(62,7) = HCF(69,62) = HCF(200,69) = HCF(1469,200) = HCF(1669,1469) = HCF(8145,1669) .

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

Step 1: Since 42060 > 1, we apply the division lemma to 42060 and 1, to get

42060 = 1 x 42060 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42060 is 1

Notice that 1 = HCF(42060,1) .

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Frequently Asked Questions on HCF of 8145, 1669, 42060 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 8145, 1669, 42060?

Answer: HCF of 8145, 1669, 42060 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8145, 1669, 42060 using Euclid's Algorithm?

Answer: For arbitrary numbers 8145, 1669, 42060 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.