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 586, 828 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 586, 828 is 2 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 586, 828 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 586, 828 is 2.
HCF(586, 828) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 586, 828 is 2.
Step 1: Since 828 > 586, we apply the division lemma to 828 and 586, to get
828 = 586 x 1 + 242
Step 2: Since the reminder 586 ≠ 0, we apply division lemma to 242 and 586, to get
586 = 242 x 2 + 102
Step 3: We consider the new divisor 242 and the new remainder 102, and apply the division lemma to get
242 = 102 x 2 + 38
We consider the new divisor 102 and the new remainder 38,and apply the division lemma to get
102 = 38 x 2 + 26
We consider the new divisor 38 and the new remainder 26,and apply the division lemma to get
38 = 26 x 1 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 586 and 828 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(38,26) = HCF(102,38) = HCF(242,102) = HCF(586,242) = HCF(828,586) .
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 586, 828?
Answer: HCF of 586, 828 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 586, 828 using Euclid's Algorithm?
Answer: For arbitrary numbers 586, 828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.