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, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 529 is 1 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, 529 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, 529 is 1.
HCF(978, 529) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 529 is 1.
Step 1: Since 978 > 529, we apply the division lemma to 978 and 529, to get
978 = 529 x 1 + 449
Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 449 and 529, to get
529 = 449 x 1 + 80
Step 3: We consider the new divisor 449 and the new remainder 80, and apply the division lemma to get
449 = 80 x 5 + 49
We consider the new divisor 80 and the new remainder 49,and apply the division lemma to get
80 = 49 x 1 + 31
We consider the new divisor 49 and the new remainder 31,and apply the division lemma to get
49 = 31 x 1 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 978 and 529 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(49,31) = HCF(80,49) = HCF(449,80) = HCF(529,449) = HCF(978,529) .
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, 529?
Answer: HCF of 978, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 529 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.