Highest Common Factor of 690, 898, 433 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 690, 898, 433 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 898, 433 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 690, 898, 433 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 690, 898, 433 is 1.

HCF(690, 898, 433) = 1

HCF of 690, 898, 433 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 690, 898, 433 is 1.

Highest Common Factor of 690,898,433 using Euclid's algorithm

Highest Common Factor of 690,898,433 is 1

Step 1: Since 898 > 690, we apply the division lemma to 898 and 690, to get

898 = 690 x 1 + 208

Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 208 and 690, to get

690 = 208 x 3 + 66

Step 3: We consider the new divisor 208 and the new remainder 66, and apply the division lemma to get

208 = 66 x 3 + 10

We consider the new divisor 66 and the new remainder 10,and apply the division lemma to get

66 = 10 x 6 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 690 and 898 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(208,66) = HCF(690,208) = HCF(898,690) .

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

Step 1: Since 433 > 2, we apply the division lemma to 433 and 2, to get

433 = 2 x 216 + 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 433 is 1

Notice that 1 = HCF(2,1) = HCF(433,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 690, 898, 433 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 690, 898, 433?

Answer: HCF of 690, 898, 433 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 898, 433 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 898, 433 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.