Highest Common Factor of 8298, 8910, 57658 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 8298, 8910, 57658 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8298, 8910, 57658 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 8298, 8910, 57658 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 8298, 8910, 57658 is 2.
HCF(8298, 8910, 57658) = 2
HCF of 8298, 8910, 57658 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8298, 8910, 57658 is 2.
Highest Common Factor of 8298,8910,57658 is 2
Step 1: Since 8910 > 8298, we apply the division lemma to 8910 and 8298, to get
8910 = 8298 x 1 + 612
Step 2: Since the reminder 8298 ≠ 0, we apply division lemma to 612 and 8298, to get
8298 = 612 x 13 + 342
Step 3: We consider the new divisor 612 and the new remainder 342, and apply the division lemma to get
612 = 342 x 1 + 270
We consider the new divisor 342 and the new remainder 270,and apply the division lemma to get
342 = 270 x 1 + 72
We consider the new divisor 270 and the new remainder 72,and apply the division lemma to get
270 = 72 x 3 + 54
We consider the new divisor 72 and the new remainder 54,and apply the division lemma to get
72 = 54 x 1 + 18
We consider the new divisor 54 and the new remainder 18,and apply the division lemma to get
54 = 18 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 8298 and 8910 is 18
Notice that 18 = HCF(54,18) = HCF(72,54) = HCF(270,72) = HCF(342,270) = HCF(612,342) = HCF(8298,612) = HCF(8910,8298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57658 > 18, we apply the division lemma to 57658 and 18, to get
57658 = 18 x 3203 + 4
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 4 and 18, to get
18 = 4 x 4 + 2
Step 3: 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 18 and 57658 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(57658,18) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8298, 8910, 57658 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 8298, 8910, 57658?
Answer: HCF of 8298, 8910, 57658 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8298, 8910, 57658 using Euclid's Algorithm?
Answer: For arbitrary numbers 8298, 8910, 57658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.