Highest Common Factor of 978, 8174 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, 8174 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 8174 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 978, 8174 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, 8174 is 2.
HCF(978, 8174) = 2
HCF of 978, 8174 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, 8174 is 2.
Highest Common Factor of 978,8174 is 2
Step 1: Since 8174 > 978, we apply the division lemma to 8174 and 978, to get
8174 = 978 x 8 + 350
Step 2: Since the reminder 978 ≠ 0, we apply division lemma to 350 and 978, to get
978 = 350 x 2 + 278
Step 3: We consider the new divisor 350 and the new remainder 278, and apply the division lemma to get
350 = 278 x 1 + 72
We consider the new divisor 278 and the new remainder 72,and apply the division lemma to get
278 = 72 x 3 + 62
We consider the new divisor 72 and the new remainder 62,and apply the division lemma to get
72 = 62 x 1 + 10
We consider the new divisor 62 and the new remainder 10,and apply the division lemma to get
62 = 10 x 6 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 978 and 8174 is 2
Notice that 2 = HCF(10,2) = HCF(62,10) = HCF(72,62) = HCF(278,72) = HCF(350,278) = HCF(978,350) = HCF(8174,978) .
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Frequently Asked Questions on HCF of 978, 8174 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, 8174?
Answer: HCF of 978, 8174 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 8174 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 8174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.