Highest Common Factor of 828, 605 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 828, 605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 605 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 828, 605 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 828, 605 is 1.
HCF(828, 605) = 1
HCF of 828, 605 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 828, 605 is 1.
Highest Common Factor of 828,605 is 1
Step 1: Since 828 > 605, we apply the division lemma to 828 and 605, to get
828 = 605 x 1 + 223
Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 223 and 605, to get
605 = 223 x 2 + 159
Step 3: We consider the new divisor 223 and the new remainder 159, and apply the division lemma to get
223 = 159 x 1 + 64
We consider the new divisor 159 and the new remainder 64,and apply the division lemma to get
159 = 64 x 2 + 31
We consider the new divisor 64 and the new remainder 31,and apply the division lemma to get
64 = 31 x 2 + 2
We consider the new divisor 31 and the new remainder 2,and apply the division lemma to get
31 = 2 x 15 + 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 828 and 605 is 1
Notice that 1 = HCF(2,1) = HCF(31,2) = HCF(64,31) = HCF(159,64) = HCF(223,159) = HCF(605,223) = HCF(828,605) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 828, 605 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 828, 605?
Answer: HCF of 828, 605 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 605 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
