Highest Common Factor of 432, 698, 619 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 432, 698, 619 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 432, 698, 619 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 432, 698, 619 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 432, 698, 619 is 1.

HCF(432, 698, 619) = 1

HCF of 432, 698, 619 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 432, 698, 619 is 1.

Highest Common Factor of 432,698,619 using Euclid's algorithm

Highest Common Factor of 432,698,619 is 1

Step 1: Since 698 > 432, we apply the division lemma to 698 and 432, to get

698 = 432 x 1 + 266

Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 266 and 432, to get

432 = 266 x 1 + 166

Step 3: We consider the new divisor 266 and the new remainder 166, and apply the division lemma to get

266 = 166 x 1 + 100

We consider the new divisor 166 and the new remainder 100,and apply the division lemma to get

166 = 100 x 1 + 66

We consider the new divisor 100 and the new remainder 66,and apply the division lemma to get

100 = 66 x 1 + 34

We consider the new divisor 66 and the new remainder 34,and apply the division lemma to get

66 = 34 x 1 + 32

We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get

34 = 32 x 1 + 2

We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get

32 = 2 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 432 and 698 is 2

Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(66,34) = HCF(100,66) = HCF(166,100) = HCF(266,166) = HCF(432,266) = HCF(698,432) .

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

Step 1: Since 619 > 2, we apply the division lemma to 619 and 2, to get

619 = 2 x 309 + 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 619 is 1

Notice that 1 = HCF(2,1) = HCF(619,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 432, 698, 619 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 432, 698, 619?

Answer: HCF of 432, 698, 619 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 432, 698, 619 using Euclid's Algorithm?

Answer: For arbitrary numbers 432, 698, 619 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.