Highest Common Factor of 8242, 9830 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 8242, 9830 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8242, 9830 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 8242, 9830 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 8242, 9830 is 2.
HCF(8242, 9830) = 2
HCF of 8242, 9830 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8242, 9830 is 2.
Highest Common Factor of 8242,9830 is 2
Step 1: Since 9830 > 8242, we apply the division lemma to 9830 and 8242, to get
9830 = 8242 x 1 + 1588
Step 2: Since the reminder 8242 ≠ 0, we apply division lemma to 1588 and 8242, to get
8242 = 1588 x 5 + 302
Step 3: We consider the new divisor 1588 and the new remainder 302, and apply the division lemma to get
1588 = 302 x 5 + 78
We consider the new divisor 302 and the new remainder 78,and apply the division lemma to get
302 = 78 x 3 + 68
We consider the new divisor 78 and the new remainder 68,and apply the division lemma to get
78 = 68 x 1 + 10
We consider the new divisor 68 and the new remainder 10,and apply the division lemma to get
68 = 10 x 6 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8242 and 9830 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(68,10) = HCF(78,68) = HCF(302,78) = HCF(1588,302) = HCF(8242,1588) = HCF(9830,8242) .
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Frequently Asked Questions on HCF of 8242, 9830 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 8242, 9830?
Answer: HCF of 8242, 9830 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8242, 9830 using Euclid's Algorithm?
Answer: For arbitrary numbers 8242, 9830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.