Highest Common Factor of 822, 416 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 822, 416 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 416 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 822, 416 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 822, 416 is 2.
HCF(822, 416) = 2
HCF of 822, 416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 416 is 2.
Highest Common Factor of 822,416 is 2
Step 1: Since 822 > 416, we apply the division lemma to 822 and 416, to get
822 = 416 x 1 + 406
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 406 and 416, to get
416 = 406 x 1 + 10
Step 3: We consider the new divisor 406 and the new remainder 10, and apply the division lemma to get
406 = 10 x 40 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 822 and 416 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(406,10) = HCF(416,406) = HCF(822,416) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 822, 416 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 822, 416?
Answer: HCF of 822, 416 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.