Highest Common Factor of 572, 918, 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 572, 918, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 572, 918, 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 572, 918, 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 572, 918, 814 is 2.
HCF(572, 918, 814) = 2
HCF of 572, 918, 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 572, 918, 814 is 2.
Highest Common Factor of 572,918,814 is 2
Step 1: Since 918 > 572, we apply the division lemma to 918 and 572, to get
918 = 572 x 1 + 346
Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 346 and 572, to get
572 = 346 x 1 + 226
Step 3: We consider the new divisor 346 and the new remainder 226, and apply the division lemma to get
346 = 226 x 1 + 120
We consider the new divisor 226 and the new remainder 120,and apply the division lemma to get
226 = 120 x 1 + 106
We consider the new divisor 120 and the new remainder 106,and apply the division lemma to get
120 = 106 x 1 + 14
We consider the new divisor 106 and the new remainder 14,and apply the division lemma to get
106 = 14 x 7 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 572 and 918 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(106,14) = HCF(120,106) = HCF(226,120) = HCF(346,226) = HCF(572,346) = HCF(918,572) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 2, we apply the division lemma to 814 and 2, to get
814 = 2 x 407 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 814 is 2
Notice that 2 = HCF(814,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 572, 918, 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 572, 918, 814?
Answer: HCF of 572, 918, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 572, 918, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 572, 918, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.