Highest Common Factor of 978, 9498 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 978, 9498 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 9498 is 6 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 978, 9498 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 978, 9498 is 6.
HCF(978, 9498) = 6
HCF of 978, 9498 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 9498 is 6.
Highest Common Factor of 978,9498 is 6
Step 1: Since 9498 > 978, we apply the division lemma to 9498 and 978, to get
9498 = 978 x 9 + 696
Step 2: Since the reminder 978 ≠ 0, we apply division lemma to 696 and 978, to get
978 = 696 x 1 + 282
Step 3: We consider the new divisor 696 and the new remainder 282, and apply the division lemma to get
696 = 282 x 2 + 132
We consider the new divisor 282 and the new remainder 132,and apply the division lemma to get
282 = 132 x 2 + 18
We consider the new divisor 132 and the new remainder 18,and apply the division lemma to get
132 = 18 x 7 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 9498 is 6
Notice that 6 = HCF(18,6) = HCF(132,18) = HCF(282,132) = HCF(696,282) = HCF(978,696) = HCF(9498,978) .
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Frequently Asked Questions on HCF of 978, 9498 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 978, 9498?
Answer: HCF of 978, 9498 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 9498 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 9498 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.