Highest Common Factor of 831, 2028 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 831, 2028 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 831, 2028 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 831, 2028 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 831, 2028 is 3.
HCF(831, 2028) = 3
HCF of 831, 2028 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 831, 2028 is 3.
Highest Common Factor of 831,2028 is 3
Step 1: Since 2028 > 831, we apply the division lemma to 2028 and 831, to get
2028 = 831 x 2 + 366
Step 2: Since the reminder 831 ≠ 0, we apply division lemma to 366 and 831, to get
831 = 366 x 2 + 99
Step 3: We consider the new divisor 366 and the new remainder 99, and apply the division lemma to get
366 = 99 x 3 + 69
We consider the new divisor 99 and the new remainder 69,and apply the division lemma to get
99 = 69 x 1 + 30
We consider the new divisor 69 and the new remainder 30,and apply the division lemma to get
69 = 30 x 2 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 831 and 2028 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(69,30) = HCF(99,69) = HCF(366,99) = HCF(831,366) = HCF(2028,831) .
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Frequently Asked Questions on HCF of 831, 2028 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 831, 2028?
Answer: HCF of 831, 2028 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 831, 2028 using Euclid's Algorithm?
Answer: For arbitrary numbers 831, 2028 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
