Highest Common Factor of 978, 536 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, 536 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 536 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, 536 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, 536 is 2.
HCF(978, 536) = 2
HCF of 978, 536 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, 536 is 2.
Highest Common Factor of 978,536 is 2
Step 1: Since 978 > 536, we apply the division lemma to 978 and 536, to get
978 = 536 x 1 + 442
Step 2: Since the reminder 536 ≠ 0, we apply division lemma to 442 and 536, to get
536 = 442 x 1 + 94
Step 3: We consider the new divisor 442 and the new remainder 94, and apply the division lemma to get
442 = 94 x 4 + 66
We consider the new divisor 94 and the new remainder 66,and apply the division lemma to get
94 = 66 x 1 + 28
We consider the new divisor 66 and the new remainder 28,and apply the division lemma to get
66 = 28 x 2 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 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 978 and 536 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(66,28) = HCF(94,66) = HCF(442,94) = HCF(536,442) = HCF(978,536) .
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Frequently Asked Questions on HCF of 978, 536 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, 536?
Answer: HCF of 978, 536 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 536 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 536 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.