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, 60082 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 60082 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, 60082 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, 60082 is 2.
HCF(978, 60082) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 60082 is 2.
Step 1: Since 60082 > 978, we apply the division lemma to 60082 and 978, to get
60082 = 978 x 61 + 424
Step 2: Since the reminder 978 ≠ 0, we apply division lemma to 424 and 978, to get
978 = 424 x 2 + 130
Step 3: We consider the new divisor 424 and the new remainder 130, and apply the division lemma to get
424 = 130 x 3 + 34
We consider the new divisor 130 and the new remainder 34,and apply the division lemma to get
130 = 34 x 3 + 28
We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get
34 = 28 x 1 + 6
We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get
28 = 6 x 4 + 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 978 and 60082 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(130,34) = HCF(424,130) = HCF(978,424) = HCF(60082,978) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 60082?
Answer: HCF of 978, 60082 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 60082 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 60082 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.