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, 610 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 610 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, 610 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, 610 is 2.
HCF(978, 610) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 610 is 2.
Step 1: Since 978 > 610, we apply the division lemma to 978 and 610, to get
978 = 610 x 1 + 368
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 368 and 610, to get
610 = 368 x 1 + 242
Step 3: We consider the new divisor 368 and the new remainder 242, and apply the division lemma to get
368 = 242 x 1 + 126
We consider the new divisor 242 and the new remainder 126,and apply the division lemma to get
242 = 126 x 1 + 116
We consider the new divisor 126 and the new remainder 116,and apply the division lemma to get
126 = 116 x 1 + 10
We consider the new divisor 116 and the new remainder 10,and apply the division lemma to get
116 = 10 x 11 + 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 978 and 610 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(116,10) = HCF(126,116) = HCF(242,126) = HCF(368,242) = HCF(610,368) = HCF(978,610) .
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, 610?
Answer: HCF of 978, 610 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 610 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.