Highest Common Factor of 530, 205, 978 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 530, 205, 978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 530, 205, 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 530, 205, 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 530, 205, 978 is 1.
HCF(530, 205, 978) = 1
HCF of 530, 205, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 530, 205, 978 is 1.
Highest Common Factor of 530,205,978 is 1
Step 1: Since 530 > 205, we apply the division lemma to 530 and 205, to get
530 = 205 x 2 + 120
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 120 and 205, to get
205 = 120 x 1 + 85
Step 3: We consider the new divisor 120 and the new remainder 85, and apply the division lemma to get
120 = 85 x 1 + 35
We consider the new divisor 85 and the new remainder 35,and apply the division lemma to get
85 = 35 x 2 + 15
We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get
35 = 15 x 2 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 530 and 205 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(85,35) = HCF(120,85) = HCF(205,120) = HCF(530,205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 5, we apply the division lemma to 978 and 5, to get
978 = 5 x 195 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: 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 5 and 978 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(978,5) .
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Frequently Asked Questions on HCF of 530, 205, 978 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 530, 205, 978?
Answer: HCF of 530, 205, 978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 530, 205, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 530, 205, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.