Highest Common Factor of 8290, 9738 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 8290, 9738 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8290, 9738 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 8290, 9738 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 8290, 9738 is 2.
HCF(8290, 9738) = 2
HCF of 8290, 9738 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8290, 9738 is 2.
Highest Common Factor of 8290,9738 is 2
Step 1: Since 9738 > 8290, we apply the division lemma to 9738 and 8290, to get
9738 = 8290 x 1 + 1448
Step 2: Since the reminder 8290 ≠ 0, we apply division lemma to 1448 and 8290, to get
8290 = 1448 x 5 + 1050
Step 3: We consider the new divisor 1448 and the new remainder 1050, and apply the division lemma to get
1448 = 1050 x 1 + 398
We consider the new divisor 1050 and the new remainder 398,and apply the division lemma to get
1050 = 398 x 2 + 254
We consider the new divisor 398 and the new remainder 254,and apply the division lemma to get
398 = 254 x 1 + 144
We consider the new divisor 254 and the new remainder 144,and apply the division lemma to get
254 = 144 x 1 + 110
We consider the new divisor 144 and the new remainder 110,and apply the division lemma to get
144 = 110 x 1 + 34
We consider the new divisor 110 and the new remainder 34,and apply the division lemma to get
110 = 34 x 3 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 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 8290 and 9738 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(110,34) = HCF(144,110) = HCF(254,144) = HCF(398,254) = HCF(1050,398) = HCF(1448,1050) = HCF(8290,1448) = HCF(9738,8290) .
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Frequently Asked Questions on HCF of 8290, 9738 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 8290, 9738?
Answer: HCF of 8290, 9738 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8290, 9738 using Euclid's Algorithm?
Answer: For arbitrary numbers 8290, 9738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.