Highest Common Factor of 2298, 2914 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 2298, 2914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2298, 2914 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 2298, 2914 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 2298, 2914 is 2.
HCF(2298, 2914) = 2
HCF of 2298, 2914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2298, 2914 is 2.
Highest Common Factor of 2298,2914 is 2
Step 1: Since 2914 > 2298, we apply the division lemma to 2914 and 2298, to get
2914 = 2298 x 1 + 616
Step 2: Since the reminder 2298 ≠ 0, we apply division lemma to 616 and 2298, to get
2298 = 616 x 3 + 450
Step 3: We consider the new divisor 616 and the new remainder 450, and apply the division lemma to get
616 = 450 x 1 + 166
We consider the new divisor 450 and the new remainder 166,and apply the division lemma to get
450 = 166 x 2 + 118
We consider the new divisor 166 and the new remainder 118,and apply the division lemma to get
166 = 118 x 1 + 48
We consider the new divisor 118 and the new remainder 48,and apply the division lemma to get
118 = 48 x 2 + 22
We consider the new divisor 48 and the new remainder 22,and apply the division lemma to get
48 = 22 x 2 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 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 2298 and 2914 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(118,48) = HCF(166,118) = HCF(450,166) = HCF(616,450) = HCF(2298,616) = HCF(2914,2298) .
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Frequently Asked Questions on HCF of 2298, 2914 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 2298, 2914?
Answer: HCF of 2298, 2914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2298, 2914 using Euclid's Algorithm?
Answer: For arbitrary numbers 2298, 2914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.