Highest Common Factor of 7572, 9285, 60594 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 7572, 9285, 60594 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 7572, 9285, 60594 is 3 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 7572, 9285, 60594 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 7572, 9285, 60594 is 3.

HCF(7572, 9285, 60594) = 3

HCF of 7572, 9285, 60594 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 7572, 9285, 60594 is 3.

Highest Common Factor of 7572,9285,60594 using Euclid's algorithm

Highest Common Factor of 7572,9285,60594 is 3

Step 1: Since 9285 > 7572, we apply the division lemma to 9285 and 7572, to get

9285 = 7572 x 1 + 1713

Step 2: Since the reminder 7572 ≠ 0, we apply division lemma to 1713 and 7572, to get

7572 = 1713 x 4 + 720

Step 3: We consider the new divisor 1713 and the new remainder 720, and apply the division lemma to get

1713 = 720 x 2 + 273

We consider the new divisor 720 and the new remainder 273,and apply the division lemma to get

720 = 273 x 2 + 174

We consider the new divisor 273 and the new remainder 174,and apply the division lemma to get

273 = 174 x 1 + 99

We consider the new divisor 174 and the new remainder 99,and apply the division lemma to get

174 = 99 x 1 + 75

We consider the new divisor 99 and the new remainder 75,and apply the division lemma to get

99 = 75 x 1 + 24

We consider the new divisor 75 and the new remainder 24,and apply the division lemma to get

75 = 24 x 3 + 3

We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get

24 = 3 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7572 and 9285 is 3

Notice that 3 = HCF(24,3) = HCF(75,24) = HCF(99,75) = HCF(174,99) = HCF(273,174) = HCF(720,273) = HCF(1713,720) = HCF(7572,1713) = HCF(9285,7572) .

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

Step 1: Since 60594 > 3, we apply the division lemma to 60594 and 3, to get

60594 = 3 x 20198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 60594 is 3

Notice that 3 = HCF(60594,3) .

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Frequently Asked Questions on HCF of 7572, 9285, 60594 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 7572, 9285, 60594?

Answer: HCF of 7572, 9285, 60594 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7572, 9285, 60594 using Euclid's Algorithm?

Answer: For arbitrary numbers 7572, 9285, 60594 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.