Highest Common Factor of 4028, 6642, 37852 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 4028, 6642, 37852 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 4028, 6642, 37852 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 4028, 6642, 37852 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 4028, 6642, 37852 is 2.
HCF(4028, 6642, 37852) = 2
HCF of 4028, 6642, 37852 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4028, 6642, 37852 is 2.
Highest Common Factor of 4028,6642,37852 is 2
Step 1: Since 6642 > 4028, we apply the division lemma to 6642 and 4028, to get
6642 = 4028 x 1 + 2614
Step 2: Since the reminder 4028 ≠ 0, we apply division lemma to 2614 and 4028, to get
4028 = 2614 x 1 + 1414
Step 3: We consider the new divisor 2614 and the new remainder 1414, and apply the division lemma to get
2614 = 1414 x 1 + 1200
We consider the new divisor 1414 and the new remainder 1200,and apply the division lemma to get
1414 = 1200 x 1 + 214
We consider the new divisor 1200 and the new remainder 214,and apply the division lemma to get
1200 = 214 x 5 + 130
We consider the new divisor 214 and the new remainder 130,and apply the division lemma to get
214 = 130 x 1 + 84
We consider the new divisor 130 and the new remainder 84,and apply the division lemma to get
130 = 84 x 1 + 46
We consider the new divisor 84 and the new remainder 46,and apply the division lemma to get
84 = 46 x 1 + 38
We consider the new divisor 46 and the new remainder 38,and apply the division lemma to get
46 = 38 x 1 + 8
We consider the new divisor 38 and the new remainder 8,and apply the division lemma to get
38 = 8 x 4 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4028 and 6642 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(46,38) = HCF(84,46) = HCF(130,84) = HCF(214,130) = HCF(1200,214) = HCF(1414,1200) = HCF(2614,1414) = HCF(4028,2614) = HCF(6642,4028) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37852 > 2, we apply the division lemma to 37852 and 2, to get
37852 = 2 x 18926 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 37852 is 2
Notice that 2 = HCF(37852,2) .
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Frequently Asked Questions on HCF of 4028, 6642, 37852 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 4028, 6642, 37852?
Answer: HCF of 4028, 6642, 37852 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4028, 6642, 37852 using Euclid's Algorithm?
Answer: For arbitrary numbers 4028, 6642, 37852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.