Highest Common Factor of 643, 978, 45 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 643, 978, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 643, 978, 45 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 643, 978, 45 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 643, 978, 45 is 1.
HCF(643, 978, 45) = 1
HCF of 643, 978, 45 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 643, 978, 45 is 1.
Highest Common Factor of 643,978,45 is 1
Step 1: Since 978 > 643, we apply the division lemma to 978 and 643, to get
978 = 643 x 1 + 335
Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 335 and 643, to get
643 = 335 x 1 + 308
Step 3: We consider the new divisor 335 and the new remainder 308, and apply the division lemma to get
335 = 308 x 1 + 27
We consider the new divisor 308 and the new remainder 27,and apply the division lemma to get
308 = 27 x 11 + 11
We consider the new divisor 27 and the new remainder 11,and apply the division lemma to get
27 = 11 x 2 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 643 and 978 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(27,11) = HCF(308,27) = HCF(335,308) = HCF(643,335) = HCF(978,643) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
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Frequently Asked Questions on HCF of 643, 978, 45 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 643, 978, 45?
Answer: HCF of 643, 978, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 643, 978, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 643, 978, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.