Highest Common Factor of 2114, 1448 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 2114, 1448 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2114, 1448 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 2114, 1448 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 2114, 1448 is 2.
HCF(2114, 1448) = 2
HCF of 2114, 1448 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2114, 1448 is 2.
Highest Common Factor of 2114,1448 is 2
Step 1: Since 2114 > 1448, we apply the division lemma to 2114 and 1448, to get
2114 = 1448 x 1 + 666
Step 2: Since the reminder 1448 ≠ 0, we apply division lemma to 666 and 1448, to get
1448 = 666 x 2 + 116
Step 3: We consider the new divisor 666 and the new remainder 116, and apply the division lemma to get
666 = 116 x 5 + 86
We consider the new divisor 116 and the new remainder 86,and apply the division lemma to get
116 = 86 x 1 + 30
We consider the new divisor 86 and the new remainder 30,and apply the division lemma to get
86 = 30 x 2 + 26
We consider the new divisor 30 and the new remainder 26,and apply the division lemma to get
30 = 26 x 1 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2114 and 1448 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(30,26) = HCF(86,30) = HCF(116,86) = HCF(666,116) = HCF(1448,666) = HCF(2114,1448) .
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Frequently Asked Questions on HCF of 2114, 1448 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 2114, 1448?
Answer: HCF of 2114, 1448 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2114, 1448 using Euclid's Algorithm?
Answer: For arbitrary numbers 2114, 1448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.