Highest Common Factor of 390, 605, 675 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 390, 605, 675 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 390, 605, 675 is 5 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 390, 605, 675 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 390, 605, 675 is 5.

HCF(390, 605, 675) = 5

HCF of 390, 605, 675 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 390, 605, 675 is 5.

Highest Common Factor of 390,605,675 using Euclid's algorithm

Highest Common Factor of 390,605,675 is 5

Step 1: Since 605 > 390, we apply the division lemma to 605 and 390, to get

605 = 390 x 1 + 215

Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 215 and 390, to get

390 = 215 x 1 + 175

Step 3: We consider the new divisor 215 and the new remainder 175, and apply the division lemma to get

215 = 175 x 1 + 40

We consider the new divisor 175 and the new remainder 40,and apply the division lemma to get

175 = 40 x 4 + 15

We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get

40 = 15 x 2 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 390 and 605 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(175,40) = HCF(215,175) = HCF(390,215) = HCF(605,390) .

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

Step 1: Since 675 > 5, we apply the division lemma to 675 and 5, to get

675 = 5 x 135 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 675 is 5

Notice that 5 = HCF(675,5) .

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Frequently Asked Questions on HCF of 390, 605, 675 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 390, 605, 675?

Answer: HCF of 390, 605, 675 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 390, 605, 675 using Euclid's Algorithm?

Answer: For arbitrary numbers 390, 605, 675 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.