Highest Common Factor of 106, 377, 127 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 106, 377, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 106, 377, 127 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 106, 377, 127 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 106, 377, 127 is 1.
HCF(106, 377, 127) = 1
HCF of 106, 377, 127 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 106, 377, 127 is 1.
Highest Common Factor of 106,377,127 is 1
Step 1: Since 377 > 106, we apply the division lemma to 377 and 106, to get
377 = 106 x 3 + 59
Step 2: Since the reminder 106 ≠ 0, we apply division lemma to 59 and 106, to get
106 = 59 x 1 + 47
Step 3: We consider the new divisor 59 and the new remainder 47, and apply the division lemma to get
59 = 47 x 1 + 12
We consider the new divisor 47 and the new remainder 12,and apply the division lemma to get
47 = 12 x 3 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 106 and 377 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(47,12) = HCF(59,47) = HCF(106,59) = HCF(377,106) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 127 > 1, we apply the division lemma to 127 and 1, to get
127 = 1 x 127 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 127 is 1
Notice that 1 = HCF(127,1) .
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Frequently Asked Questions on HCF of 106, 377, 127 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 106, 377, 127?
Answer: HCF of 106, 377, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 106, 377, 127 using Euclid's Algorithm?
Answer: For arbitrary numbers 106, 377, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.