Highest Common Factor of 822, 660, 229 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 822, 660, 229 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 660, 229 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 822, 660, 229 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 822, 660, 229 is 1.
HCF(822, 660, 229) = 1
HCF of 822, 660, 229 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 660, 229 is 1.
Highest Common Factor of 822,660,229 is 1
Step 1: Since 822 > 660, we apply the division lemma to 822 and 660, to get
822 = 660 x 1 + 162
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 162 and 660, to get
660 = 162 x 4 + 12
Step 3: We consider the new divisor 162 and the new remainder 12, and apply the division lemma to get
162 = 12 x 13 + 6
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 822 and 660 is 6
Notice that 6 = HCF(12,6) = HCF(162,12) = HCF(660,162) = HCF(822,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 229 > 6, we apply the division lemma to 229 and 6, to get
229 = 6 x 38 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 229 is 1
Notice that 1 = HCF(6,1) = HCF(229,6) .
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Frequently Asked Questions on HCF of 822, 660, 229 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 822, 660, 229?
Answer: HCF of 822, 660, 229 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 660, 229 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 660, 229 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.