Highest Common Factor of 354, 814 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 354, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 814 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 354, 814 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 354, 814 is 2.
HCF(354, 814) = 2
HCF of 354, 814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 814 is 2.
Highest Common Factor of 354,814 is 2
Step 1: Since 814 > 354, we apply the division lemma to 814 and 354, to get
814 = 354 x 2 + 106
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 106 and 354, to get
354 = 106 x 3 + 36
Step 3: We consider the new divisor 106 and the new remainder 36, and apply the division lemma to get
106 = 36 x 2 + 34
We consider the new divisor 36 and the new remainder 34,and apply the division lemma to get
36 = 34 x 1 + 2
We consider the new divisor 34 and the new remainder 2,and apply the division lemma to get
34 = 2 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 814 is 2
Notice that 2 = HCF(34,2) = HCF(36,34) = HCF(106,36) = HCF(354,106) = HCF(814,354) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 354, 814 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 354, 814?
Answer: HCF of 354, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.