Highest Common Factor of 388, 978 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 388, 978 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 388, 978 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 388, 978 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 388, 978 is 2.
HCF(388, 978) = 2
HCF of 388, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 388, 978 is 2.
Highest Common Factor of 388,978 is 2
Step 1: Since 978 > 388, we apply the division lemma to 978 and 388, to get
978 = 388 x 2 + 202
Step 2: Since the reminder 388 ≠ 0, we apply division lemma to 202 and 388, to get
388 = 202 x 1 + 186
Step 3: We consider the new divisor 202 and the new remainder 186, and apply the division lemma to get
202 = 186 x 1 + 16
We consider the new divisor 186 and the new remainder 16,and apply the division lemma to get
186 = 16 x 11 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 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 388 and 978 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(186,16) = HCF(202,186) = HCF(388,202) = HCF(978,388) .
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Frequently Asked Questions on HCF of 388, 978 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 388, 978?
Answer: HCF of 388, 978 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 388, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 388, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.