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 813, 531, 617, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 813, 531, 617, 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 813, 531, 617, 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 813, 531, 617, 823 is 1.
HCF(813, 531, 617, 823) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 813, 531, 617, 823 is 1.
Step 1: Since 813 > 531, we apply the division lemma to 813 and 531, to get
813 = 531 x 1 + 282
Step 2: Since the reminder 531 ≠ 0, we apply division lemma to 282 and 531, to get
531 = 282 x 1 + 249
Step 3: We consider the new divisor 282 and the new remainder 249, and apply the division lemma to get
282 = 249 x 1 + 33
We consider the new divisor 249 and the new remainder 33,and apply the division lemma to get
249 = 33 x 7 + 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 813 and 531 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(249,33) = HCF(282,249) = HCF(531,282) = HCF(813,531) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 617 > 3, we apply the division lemma to 617 and 3, to get
617 = 3 x 205 + 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 617 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(617,3) .
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 813, 531, 617, 823?
Answer: HCF of 813, 531, 617, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 813, 531, 617, 823 using Euclid's Algorithm?
Answer: For arbitrary numbers 813, 531, 617, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.