Highest Common Factor of 390, 538, 67 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, 538, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 390, 538, 67 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 390, 538, 67 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, 538, 67 is 1.

HCF(390, 538, 67) = 1

HCF of 390, 538, 67 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, 538, 67 is 1.

Highest Common Factor of 390,538,67 using Euclid's algorithm

Highest Common Factor of 390,538,67 is 1

Step 1: Since 538 > 390, we apply the division lemma to 538 and 390, to get

538 = 390 x 1 + 148

Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 148 and 390, to get

390 = 148 x 2 + 94

Step 3: We consider the new divisor 148 and the new remainder 94, and apply the division lemma to get

148 = 94 x 1 + 54

We consider the new divisor 94 and the new remainder 54,and apply the division lemma to get

94 = 54 x 1 + 40

We consider the new divisor 54 and the new remainder 40,and apply the division lemma to get

54 = 40 x 1 + 14

We consider the new divisor 40 and the new remainder 14,and apply the division lemma to get

40 = 14 x 2 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 390 and 538 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(40,14) = HCF(54,40) = HCF(94,54) = HCF(148,94) = HCF(390,148) = HCF(538,390) .

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

Step 1: Since 67 > 2, we apply the division lemma to 67 and 2, to get

67 = 2 x 33 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 67 is 1

Notice that 1 = HCF(2,1) = HCF(67,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 390, 538, 67 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, 538, 67?

Answer: HCF of 390, 538, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 390, 538, 67 using Euclid's Algorithm?

Answer: For arbitrary numbers 390, 538, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.