Highest Common Factor of 188, 306, 111 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 188, 306, 111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 188, 306, 111 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 188, 306, 111 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 188, 306, 111 is 1.
HCF(188, 306, 111) = 1
HCF of 188, 306, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 188, 306, 111 is 1.
Highest Common Factor of 188,306,111 is 1
Step 1: Since 306 > 188, we apply the division lemma to 306 and 188, to get
306 = 188 x 1 + 118
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 118 and 188, to get
188 = 118 x 1 + 70
Step 3: We consider the new divisor 118 and the new remainder 70, and apply the division lemma to get
118 = 70 x 1 + 48
We consider the new divisor 70 and the new remainder 48,and apply the division lemma to get
70 = 48 x 1 + 22
We consider the new divisor 48 and the new remainder 22,and apply the division lemma to get
48 = 22 x 2 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 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 188 and 306 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(70,48) = HCF(118,70) = HCF(188,118) = HCF(306,188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 2, we apply the division lemma to 111 and 2, to get
111 = 2 x 55 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 111 is 1
Notice that 1 = HCF(2,1) = HCF(111,2) .
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Frequently Asked Questions on HCF of 188, 306, 111 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 188, 306, 111?
Answer: HCF of 188, 306, 111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 188, 306, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 188, 306, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.