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 2098, 5018 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2098, 5018 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 2098, 5018 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 2098, 5018 is 2.
HCF(2098, 5018) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2098, 5018 is 2.
Step 1: Since 5018 > 2098, we apply the division lemma to 5018 and 2098, to get
5018 = 2098 x 2 + 822
Step 2: Since the reminder 2098 ≠ 0, we apply division lemma to 822 and 2098, to get
2098 = 822 x 2 + 454
Step 3: We consider the new divisor 822 and the new remainder 454, and apply the division lemma to get
822 = 454 x 1 + 368
We consider the new divisor 454 and the new remainder 368,and apply the division lemma to get
454 = 368 x 1 + 86
We consider the new divisor 368 and the new remainder 86,and apply the division lemma to get
368 = 86 x 4 + 24
We consider the new divisor 86 and the new remainder 24,and apply the division lemma to get
86 = 24 x 3 + 14
We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get
24 = 14 x 1 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 2098 and 5018 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(86,24) = HCF(368,86) = HCF(454,368) = HCF(822,454) = HCF(2098,822) = HCF(5018,2098) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 2098, 5018?
Answer: HCF of 2098, 5018 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2098, 5018 using Euclid's Algorithm?
Answer: For arbitrary numbers 2098, 5018 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.