Highest Common Factor of 821, 308 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 821, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 308 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 821, 308 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 821, 308 is 1.
HCF(821, 308) = 1
HCF of 821, 308 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 308 is 1.
Highest Common Factor of 821,308 is 1
Step 1: Since 821 > 308, we apply the division lemma to 821 and 308, to get
821 = 308 x 2 + 205
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 205 and 308, to get
308 = 205 x 1 + 103
Step 3: We consider the new divisor 205 and the new remainder 103, and apply the division lemma to get
205 = 103 x 1 + 102
We consider the new divisor 103 and the new remainder 102,and apply the division lemma to get
103 = 102 x 1 + 1
We consider the new divisor 102 and the new remainder 1,and apply the division lemma to get
102 = 1 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 308 is 1
Notice that 1 = HCF(102,1) = HCF(103,102) = HCF(205,103) = HCF(308,205) = HCF(821,308) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 821, 308 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 821, 308?
Answer: HCF of 821, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.