Highest Common Factor of 266, 414, 107 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 266, 414, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 266, 414, 107 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 266, 414, 107 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 266, 414, 107 is 1.
HCF(266, 414, 107) = 1
HCF of 266, 414, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 266, 414, 107 is 1.
Highest Common Factor of 266,414,107 is 1
Step 1: Since 414 > 266, we apply the division lemma to 414 and 266, to get
414 = 266 x 1 + 148
Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 148 and 266, to get
266 = 148 x 1 + 118
Step 3: We consider the new divisor 148 and the new remainder 118, and apply the division lemma to get
148 = 118 x 1 + 30
We consider the new divisor 118 and the new remainder 30,and apply the division lemma to get
118 = 30 x 3 + 28
We consider the new divisor 30 and the new remainder 28,and apply the division lemma to get
30 = 28 x 1 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 266 and 414 is 2
Notice that 2 = HCF(28,2) = HCF(30,28) = HCF(118,30) = HCF(148,118) = HCF(266,148) = HCF(414,266) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 2, we apply the division lemma to 107 and 2, to get
107 = 2 x 53 + 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 107 is 1
Notice that 1 = HCF(2,1) = HCF(107,2) .
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Frequently Asked Questions on HCF of 266, 414, 107 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 266, 414, 107?
Answer: HCF of 266, 414, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 266, 414, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 266, 414, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.