Highest Common Factor of 814, 336 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 814, 336 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 336 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 814, 336 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 814, 336 is 2.
HCF(814, 336) = 2
HCF of 814, 336 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 336 is 2.
Highest Common Factor of 814,336 is 2
Step 1: Since 814 > 336, we apply the division lemma to 814 and 336, to get
814 = 336 x 2 + 142
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 142 and 336, to get
336 = 142 x 2 + 52
Step 3: We consider the new divisor 142 and the new remainder 52, and apply the division lemma to get
142 = 52 x 2 + 38
We consider the new divisor 52 and the new remainder 38,and apply the division lemma to get
52 = 38 x 1 + 14
We consider the new divisor 38 and the new remainder 14,and apply the division lemma to get
38 = 14 x 2 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 814 and 336 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(38,14) = HCF(52,38) = HCF(142,52) = HCF(336,142) = HCF(814,336) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 814, 336 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 814, 336?
Answer: HCF of 814, 336 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 336 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 336 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.