Highest Common Factor of 2014, 1888 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 2014, 1888 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2014, 1888 is 2 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 2014, 1888 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 2014, 1888 is 2.
HCF(2014, 1888) = 2
HCF of 2014, 1888 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2014, 1888 is 2.
Highest Common Factor of 2014,1888 is 2
Step 1: Since 2014 > 1888, we apply the division lemma to 2014 and 1888, to get
2014 = 1888 x 1 + 126
Step 2: Since the reminder 1888 ≠ 0, we apply division lemma to 126 and 1888, to get
1888 = 126 x 14 + 124
Step 3: We consider the new divisor 126 and the new remainder 124, and apply the division lemma to get
126 = 124 x 1 + 2
We consider the new divisor 124 and the new remainder 2, and apply the division lemma to get
124 = 2 x 62 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2014 and 1888 is 2
Notice that 2 = HCF(124,2) = HCF(126,124) = HCF(1888,126) = HCF(2014,1888) .
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Frequently Asked Questions on HCF of 2014, 1888 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 2014, 1888?
Answer: HCF of 2014, 1888 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2014, 1888 using Euclid's Algorithm?
Answer: For arbitrary numbers 2014, 1888 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.