Highest Common Factor of 128, 2051 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 128, 2051 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 128, 2051 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 128, 2051 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 128, 2051 is 1.
HCF(128, 2051) = 1
HCF of 128, 2051 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 128, 2051 is 1.
Highest Common Factor of 128,2051 is 1
Step 1: Since 2051 > 128, we apply the division lemma to 2051 and 128, to get
2051 = 128 x 16 + 3
Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 3 and 128, to get
128 = 3 x 42 + 2
Step 3: 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 128 and 2051 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(128,3) = HCF(2051,128) .
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Frequently Asked Questions on HCF of 128, 2051 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 128, 2051?
Answer: HCF of 128, 2051 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 128, 2051 using Euclid's Algorithm?
Answer: For arbitrary numbers 128, 2051 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.