Highest Common Factor of 1821, 489 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 1821, 489 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1821, 489 is 3 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 1821, 489 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 1821, 489 is 3.
HCF(1821, 489) = 3
HCF of 1821, 489 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1821, 489 is 3.
Highest Common Factor of 1821,489 is 3
Step 1: Since 1821 > 489, we apply the division lemma to 1821 and 489, to get
1821 = 489 x 3 + 354
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 354 and 489, to get
489 = 354 x 1 + 135
Step 3: We consider the new divisor 354 and the new remainder 135, and apply the division lemma to get
354 = 135 x 2 + 84
We consider the new divisor 135 and the new remainder 84,and apply the division lemma to get
135 = 84 x 1 + 51
We consider the new divisor 84 and the new remainder 51,and apply the division lemma to get
84 = 51 x 1 + 33
We consider the new divisor 51 and the new remainder 33,and apply the division lemma to get
51 = 33 x 1 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1821 and 489 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(84,51) = HCF(135,84) = HCF(354,135) = HCF(489,354) = HCF(1821,489) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1821, 489 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 1821, 489?
Answer: HCF of 1821, 489 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1821, 489 using Euclid's Algorithm?
Answer: For arbitrary numbers 1821, 489 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.