Highest Common Factor of 3745, 8523, 17142 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 3745, 8523, 17142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3745, 8523, 17142 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 3745, 8523, 17142 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 3745, 8523, 17142 is 1.

HCF(3745, 8523, 17142) = 1

HCF of 3745, 8523, 17142 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 3745, 8523, 17142 is 1.

Highest Common Factor of 3745,8523,17142 using Euclid's algorithm

Highest Common Factor of 3745,8523,17142 is 1

Step 1: Since 8523 > 3745, we apply the division lemma to 8523 and 3745, to get

8523 = 3745 x 2 + 1033

Step 2: Since the reminder 3745 ≠ 0, we apply division lemma to 1033 and 3745, to get

3745 = 1033 x 3 + 646

Step 3: We consider the new divisor 1033 and the new remainder 646, and apply the division lemma to get

1033 = 646 x 1 + 387

We consider the new divisor 646 and the new remainder 387,and apply the division lemma to get

646 = 387 x 1 + 259

We consider the new divisor 387 and the new remainder 259,and apply the division lemma to get

387 = 259 x 1 + 128

We consider the new divisor 259 and the new remainder 128,and apply the division lemma to get

259 = 128 x 2 + 3

We consider the new divisor 128 and the new remainder 3,and apply the division lemma to get

128 = 3 x 42 + 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 3745 and 8523 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(128,3) = HCF(259,128) = HCF(387,259) = HCF(646,387) = HCF(1033,646) = HCF(3745,1033) = HCF(8523,3745) .

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

Step 1: Since 17142 > 1, we apply the division lemma to 17142 and 1, to get

17142 = 1 x 17142 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 17142 is 1

Notice that 1 = HCF(17142,1) .

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Frequently Asked Questions on HCF of 3745, 8523, 17142 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 3745, 8523, 17142?

Answer: HCF of 3745, 8523, 17142 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3745, 8523, 17142 using Euclid's Algorithm?

Answer: For arbitrary numbers 3745, 8523, 17142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.