Highest Common Factor of 185, 2152, 5665 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 185, 2152, 5665 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 185, 2152, 5665 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 185, 2152, 5665 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 185, 2152, 5665 is 1.
HCF(185, 2152, 5665) = 1
HCF of 185, 2152, 5665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 185, 2152, 5665 is 1.
Highest Common Factor of 185,2152,5665 is 1
Step 1: Since 2152 > 185, we apply the division lemma to 2152 and 185, to get
2152 = 185 x 11 + 117
Step 2: Since the reminder 185 ≠ 0, we apply division lemma to 117 and 185, to get
185 = 117 x 1 + 68
Step 3: We consider the new divisor 117 and the new remainder 68, and apply the division lemma to get
117 = 68 x 1 + 49
We consider the new divisor 68 and the new remainder 49,and apply the division lemma to get
68 = 49 x 1 + 19
We consider the new divisor 49 and the new remainder 19,and apply the division lemma to get
49 = 19 x 2 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 185 and 2152 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(49,19) = HCF(68,49) = HCF(117,68) = HCF(185,117) = HCF(2152,185) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5665 > 1, we apply the division lemma to 5665 and 1, to get
5665 = 1 x 5665 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5665 is 1
Notice that 1 = HCF(5665,1) .
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Frequently Asked Questions on HCF of 185, 2152, 5665 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 185, 2152, 5665?
Answer: HCF of 185, 2152, 5665 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 185, 2152, 5665 using Euclid's Algorithm?
Answer: For arbitrary numbers 185, 2152, 5665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.