Highest Common Factor of 7245, 7874, 66642 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 7245, 7874, 66642 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7245, 7874, 66642 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 7245, 7874, 66642 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 7245, 7874, 66642 is 1.

HCF(7245, 7874, 66642) = 1

HCF of 7245, 7874, 66642 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 7245, 7874, 66642 is 1.

Highest Common Factor of 7245,7874,66642 using Euclid's algorithm

Highest Common Factor of 7245,7874,66642 is 1

Step 1: Since 7874 > 7245, we apply the division lemma to 7874 and 7245, to get

7874 = 7245 x 1 + 629

Step 2: Since the reminder 7245 ≠ 0, we apply division lemma to 629 and 7245, to get

7245 = 629 x 11 + 326

Step 3: We consider the new divisor 629 and the new remainder 326, and apply the division lemma to get

629 = 326 x 1 + 303

We consider the new divisor 326 and the new remainder 303,and apply the division lemma to get

326 = 303 x 1 + 23

We consider the new divisor 303 and the new remainder 23,and apply the division lemma to get

303 = 23 x 13 + 4

We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get

23 = 4 x 5 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7245 and 7874 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(303,23) = HCF(326,303) = HCF(629,326) = HCF(7245,629) = HCF(7874,7245) .

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

Step 1: Since 66642 > 1, we apply the division lemma to 66642 and 1, to get

66642 = 1 x 66642 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66642 is 1

Notice that 1 = HCF(66642,1) .

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Frequently Asked Questions on HCF of 7245, 7874, 66642 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 7245, 7874, 66642?

Answer: HCF of 7245, 7874, 66642 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7245, 7874, 66642 using Euclid's Algorithm?

Answer: For arbitrary numbers 7245, 7874, 66642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.