Highest Common Factor of 814, 649, 643 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, 649, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 649, 643 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 814, 649, 643 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, 649, 643 is 1.
HCF(814, 649, 643) = 1
HCF of 814, 649, 643 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, 649, 643 is 1.
Highest Common Factor of 814,649,643 is 1
Step 1: Since 814 > 649, we apply the division lemma to 814 and 649, to get
814 = 649 x 1 + 165
Step 2: Since the reminder 649 ≠ 0, we apply division lemma to 165 and 649, to get
649 = 165 x 3 + 154
Step 3: We consider the new divisor 165 and the new remainder 154, and apply the division lemma to get
165 = 154 x 1 + 11
We consider the new divisor 154 and the new remainder 11, and apply the division lemma to get
154 = 11 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 814 and 649 is 11
Notice that 11 = HCF(154,11) = HCF(165,154) = HCF(649,165) = HCF(814,649) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 643 > 11, we apply the division lemma to 643 and 11, to get
643 = 11 x 58 + 5
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 5 and 11, to get
11 = 5 x 2 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 643 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(643,11) .
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, 649, 643 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, 649, 643?
Answer: HCF of 814, 649, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 649, 643 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 649, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.