Highest Common Factor of 720, 822, 411 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 720, 822, 411 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 822, 411 is 3 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 720, 822, 411 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 720, 822, 411 is 3.
HCF(720, 822, 411) = 3
HCF of 720, 822, 411 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 822, 411 is 3.
Highest Common Factor of 720,822,411 is 3
Step 1: Since 822 > 720, we apply the division lemma to 822 and 720, to get
822 = 720 x 1 + 102
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 102 and 720, to get
720 = 102 x 7 + 6
Step 3: We consider the new divisor 102 and the new remainder 6, and apply the division lemma to get
102 = 6 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 720 and 822 is 6
Notice that 6 = HCF(102,6) = HCF(720,102) = HCF(822,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 411 > 6, we apply the division lemma to 411 and 6, to get
411 = 6 x 68 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 411 is 3
Notice that 3 = HCF(6,3) = HCF(411,6) .
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Frequently Asked Questions on HCF of 720, 822, 411 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 720, 822, 411?
Answer: HCF of 720, 822, 411 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 822, 411 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 822, 411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.