Highest Common Factor of 978, 612, 514 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, 612, 514 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 612, 514 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, 612, 514 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, 612, 514 is 2.
HCF(978, 612, 514) = 2
HCF of 978, 612, 514 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, 612, 514 is 2.
Highest Common Factor of 978,612,514 is 2
Step 1: Since 978 > 612, we apply the division lemma to 978 and 612, to get
978 = 612 x 1 + 366
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 366 and 612, to get
612 = 366 x 1 + 246
Step 3: We consider the new divisor 366 and the new remainder 246, and apply the division lemma to get
366 = 246 x 1 + 120
We consider the new divisor 246 and the new remainder 120,and apply the division lemma to get
246 = 120 x 2 + 6
We consider the new divisor 120 and the new remainder 6,and apply the division lemma to get
120 = 6 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 978 and 612 is 6
Notice that 6 = HCF(120,6) = HCF(246,120) = HCF(366,246) = HCF(612,366) = HCF(978,612) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 6, we apply the division lemma to 514 and 6, to get
514 = 6 x 85 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 514 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(514,6) .
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Frequently Asked Questions on HCF of 978, 612, 514 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, 612, 514?
Answer: HCF of 978, 612, 514 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 612, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 612, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.