Highest Common Factor of 660, 209, 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 660, 209, 822 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 209, 822 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 660, 209, 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 660, 209, 822 is 1.
HCF(660, 209, 822) = 1
HCF of 660, 209, 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 660, 209, 822 is 1.
Highest Common Factor of 660,209,822 is 1
Step 1: Since 660 > 209, we apply the division lemma to 660 and 209, to get
660 = 209 x 3 + 33
Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 33 and 209, to get
209 = 33 x 6 + 11
Step 3: We consider the new divisor 33 and the new remainder 11, and apply the division lemma to get
33 = 11 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 660 and 209 is 11
Notice that 11 = HCF(33,11) = HCF(209,33) = HCF(660,209) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 11, we apply the division lemma to 822 and 11, to get
822 = 11 x 74 + 8
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get
11 = 8 x 1 + 3
Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 822 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(822,11) .
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Frequently Asked Questions on HCF of 660, 209, 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 660, 209, 822?
Answer: HCF of 660, 209, 822 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 209, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 209, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.