Highest Common Factor of 830, 548, 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 830, 548, 822 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 830, 548, 822 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 830, 548, 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 830, 548, 822 is 2.
HCF(830, 548, 822) = 2
HCF of 830, 548, 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 830, 548, 822 is 2.
Highest Common Factor of 830,548,822 is 2
Step 1: Since 830 > 548, we apply the division lemma to 830 and 548, to get
830 = 548 x 1 + 282
Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 282 and 548, to get
548 = 282 x 1 + 266
Step 3: We consider the new divisor 282 and the new remainder 266, and apply the division lemma to get
282 = 266 x 1 + 16
We consider the new divisor 266 and the new remainder 16,and apply the division lemma to get
266 = 16 x 16 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 830 and 548 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(266,16) = HCF(282,266) = HCF(548,282) = HCF(830,548) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 822 > 2, we apply the division lemma to 822 and 2, to get
822 = 2 x 411 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 822 is 2
Notice that 2 = HCF(822,2) .
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Frequently Asked Questions on HCF of 830, 548, 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 830, 548, 822?
Answer: HCF of 830, 548, 822 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 830, 548, 822 using Euclid's Algorithm?
Answer: For arbitrary numbers 830, 548, 822 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
