Highest Common Factor of 9732, 8498 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 9732, 8498 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9732, 8498 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 9732, 8498 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 9732, 8498 is 2.
HCF(9732, 8498) = 2
HCF of 9732, 8498 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9732, 8498 is 2.
Highest Common Factor of 9732,8498 is 2
Step 1: Since 9732 > 8498, we apply the division lemma to 9732 and 8498, to get
9732 = 8498 x 1 + 1234
Step 2: Since the reminder 8498 ≠ 0, we apply division lemma to 1234 and 8498, to get
8498 = 1234 x 6 + 1094
Step 3: We consider the new divisor 1234 and the new remainder 1094, and apply the division lemma to get
1234 = 1094 x 1 + 140
We consider the new divisor 1094 and the new remainder 140,and apply the division lemma to get
1094 = 140 x 7 + 114
We consider the new divisor 140 and the new remainder 114,and apply the division lemma to get
140 = 114 x 1 + 26
We consider the new divisor 114 and the new remainder 26,and apply the division lemma to get
114 = 26 x 4 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 9732 and 8498 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(114,26) = HCF(140,114) = HCF(1094,140) = HCF(1234,1094) = HCF(8498,1234) = HCF(9732,8498) .
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Frequently Asked Questions on HCF of 9732, 8498 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 9732, 8498?
Answer: HCF of 9732, 8498 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9732, 8498 using Euclid's Algorithm?
Answer: For arbitrary numbers 9732, 8498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
