Highest Common Factor of 2054, 5252, 27138 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 2054, 5252, 27138 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2054, 5252, 27138 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 2054, 5252, 27138 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 2054, 5252, 27138 is 2.
HCF(2054, 5252, 27138) = 2
HCF of 2054, 5252, 27138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2054, 5252, 27138 is 2.
Highest Common Factor of 2054,5252,27138 is 2
Step 1: Since 5252 > 2054, we apply the division lemma to 5252 and 2054, to get
5252 = 2054 x 2 + 1144
Step 2: Since the reminder 2054 ≠ 0, we apply division lemma to 1144 and 2054, to get
2054 = 1144 x 1 + 910
Step 3: We consider the new divisor 1144 and the new remainder 910, and apply the division lemma to get
1144 = 910 x 1 + 234
We consider the new divisor 910 and the new remainder 234,and apply the division lemma to get
910 = 234 x 3 + 208
We consider the new divisor 234 and the new remainder 208,and apply the division lemma to get
234 = 208 x 1 + 26
We consider the new divisor 208 and the new remainder 26,and apply the division lemma to get
208 = 26 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 2054 and 5252 is 26
Notice that 26 = HCF(208,26) = HCF(234,208) = HCF(910,234) = HCF(1144,910) = HCF(2054,1144) = HCF(5252,2054) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27138 > 26, we apply the division lemma to 27138 and 26, to get
27138 = 26 x 1043 + 20
Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 20 and 26, to get
26 = 20 x 1 + 6
Step 3: We consider the new divisor 20 and the new remainder 6, and apply the division lemma to get
20 = 6 x 3 + 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 26 and 27138 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(27138,26) .
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Frequently Asked Questions on HCF of 2054, 5252, 27138 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 2054, 5252, 27138?
Answer: HCF of 2054, 5252, 27138 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2054, 5252, 27138 using Euclid's Algorithm?
Answer: For arbitrary numbers 2054, 5252, 27138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.