Highest Common Factor of 127, 1678 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 127, 1678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 127, 1678 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 127, 1678 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 127, 1678 is 1.
HCF(127, 1678) = 1
HCF of 127, 1678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 127, 1678 is 1.
Highest Common Factor of 127,1678 is 1
Step 1: Since 1678 > 127, we apply the division lemma to 1678 and 127, to get
1678 = 127 x 13 + 27
Step 2: Since the reminder 127 ≠ 0, we apply division lemma to 27 and 127, to get
127 = 27 x 4 + 19
Step 3: We consider the new divisor 27 and the new remainder 19, and apply the division lemma to get
27 = 19 x 1 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 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 127 and 1678 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(127,27) = HCF(1678,127) .
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Frequently Asked Questions on HCF of 127, 1678 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 127, 1678?
Answer: HCF of 127, 1678 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 127, 1678 using Euclid's Algorithm?
Answer: For arbitrary numbers 127, 1678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.