Highest Common Factor of 118, 191, 216, 266 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 118, 191, 216, 266 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 118, 191, 216, 266 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 118, 191, 216, 266 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 118, 191, 216, 266 is 1.
HCF(118, 191, 216, 266) = 1
HCF of 118, 191, 216, 266 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 118, 191, 216, 266 is 1.
Highest Common Factor of 118,191,216,266 is 1
Step 1: Since 191 > 118, we apply the division lemma to 191 and 118, to get
191 = 118 x 1 + 73
Step 2: Since the reminder 118 ≠ 0, we apply division lemma to 73 and 118, to get
118 = 73 x 1 + 45
Step 3: We consider the new divisor 73 and the new remainder 45, and apply the division lemma to get
73 = 45 x 1 + 28
We consider the new divisor 45 and the new remainder 28,and apply the division lemma to get
45 = 28 x 1 + 17
We consider the new divisor 28 and the new remainder 17,and apply the division lemma to get
28 = 17 x 1 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 118 and 191 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(45,28) = HCF(73,45) = HCF(118,73) = HCF(191,118) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 216 > 1, we apply the division lemma to 216 and 1, to get
216 = 1 x 216 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 216 is 1
Notice that 1 = HCF(216,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 266 > 1, we apply the division lemma to 266 and 1, to get
266 = 1 x 266 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 266 is 1
Notice that 1 = HCF(266,1) .
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Frequently Asked Questions on HCF of 118, 191, 216, 266 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 118, 191, 216, 266?
Answer: HCF of 118, 191, 216, 266 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 118, 191, 216, 266 using Euclid's Algorithm?
Answer: For arbitrary numbers 118, 191, 216, 266 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
