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 960, 529, 978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 960, 529, 978 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 960, 529, 978 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 960, 529, 978 is 1.
HCF(960, 529, 978) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 960, 529, 978 is 1.
Step 1: Since 960 > 529, we apply the division lemma to 960 and 529, to get
960 = 529 x 1 + 431
Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 431 and 529, to get
529 = 431 x 1 + 98
Step 3: We consider the new divisor 431 and the new remainder 98, and apply the division lemma to get
431 = 98 x 4 + 39
We consider the new divisor 98 and the new remainder 39,and apply the division lemma to get
98 = 39 x 2 + 20
We consider the new divisor 39 and the new remainder 20,and apply the division lemma to get
39 = 20 x 1 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 960 and 529 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(39,20) = HCF(98,39) = HCF(431,98) = HCF(529,431) = HCF(960,529) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 1, we apply the division lemma to 978 and 1, to get
978 = 1 x 978 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 978 is 1
Notice that 1 = HCF(978,1) .
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 960, 529, 978?
Answer: HCF of 960, 529, 978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 960, 529, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 960, 529, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.