Highest Common Factor of 576, 270, 822 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 576, 270, 822 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 576, 270, 822 is 6 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 576, 270, 822 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 576, 270, 822 is 6.
HCF(576, 270, 822) = 6
HCF of 576, 270, 822 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 576, 270, 822 is 6.
Highest Common Factor of 576,270,822 is 6
Step 1: Since 576 > 270, we apply the division lemma to 576 and 270, to get
576 = 270 x 2 + 36
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 36 and 270, to get
270 = 36 x 7 + 18
Step 3: We consider the new divisor 36 and the new remainder 18, and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 576 and 270 is 18
Notice that 18 = HCF(36,18) = HCF(270,36) = HCF(576,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 18, we apply the division lemma to 822 and 18, to get
822 = 18 x 45 + 12
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 12 and 18, to get
18 = 12 x 1 + 6
Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 822 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(822,18) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 576, 270, 822 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 576, 270, 822?
Answer: HCF of 576, 270, 822 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 576, 270, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 576, 270, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.