Highest Common Factor of 135, 642, 635, 12 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 135, 642, 635, 12 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 135, 642, 635, 12 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 135, 642, 635, 12 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 135, 642, 635, 12 is 1.

HCF(135, 642, 635, 12) = 1

HCF of 135, 642, 635, 12 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 135, 642, 635, 12 is 1.

Highest Common Factor of 135,642,635,12 using Euclid's algorithm

Highest Common Factor of 135,642,635,12 is 1

Step 1: Since 642 > 135, we apply the division lemma to 642 and 135, to get

642 = 135 x 4 + 102

Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 102 and 135, to get

135 = 102 x 1 + 33

Step 3: We consider the new divisor 102 and the new remainder 33, and apply the division lemma to get

102 = 33 x 3 + 3

We consider the new divisor 33 and the new remainder 3, and apply the division lemma to get

33 = 3 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 135 and 642 is 3

Notice that 3 = HCF(33,3) = HCF(102,33) = HCF(135,102) = HCF(642,135) .

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

Step 1: Since 635 > 3, we apply the division lemma to 635 and 3, to get

635 = 3 x 211 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 635 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(635,3) .

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

Step 1: Since 12 > 1, we apply the division lemma to 12 and 1, to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12 is 1

Notice that 1 = HCF(12,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 135, 642, 635, 12 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 135, 642, 635, 12?

Answer: HCF of 135, 642, 635, 12 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 135, 642, 635, 12 using Euclid's Algorithm?

Answer: For arbitrary numbers 135, 642, 635, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.