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 242, 585, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 242, 585, 823 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 242, 585, 823 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 242, 585, 823 is 1.
HCF(242, 585, 823) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 242, 585, 823 is 1.
Step 1: Since 585 > 242, we apply the division lemma to 585 and 242, to get
585 = 242 x 2 + 101
Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 101 and 242, to get
242 = 101 x 2 + 40
Step 3: We consider the new divisor 101 and the new remainder 40, and apply the division lemma to get
101 = 40 x 2 + 21
We consider the new divisor 40 and the new remainder 21,and apply the division lemma to get
40 = 21 x 1 + 19
We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get
21 = 19 x 1 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 1
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 242 and 585 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) = HCF(101,40) = HCF(242,101) = HCF(585,242) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 823 > 1, we apply the division lemma to 823 and 1, to get
823 = 1 x 823 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 823 is 1
Notice that 1 = HCF(823,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 242, 585, 823?
Answer: HCF of 242, 585, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 242, 585, 823 using Euclid's Algorithm?
Answer: For arbitrary numbers 242, 585, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.