Highest Common Factor of 398, 978, 571, 53 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 398, 978, 571, 53 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 398, 978, 571, 53 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 398, 978, 571, 53 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 398, 978, 571, 53 is 1.
HCF(398, 978, 571, 53) = 1
HCF of 398, 978, 571, 53 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 398, 978, 571, 53 is 1.
Highest Common Factor of 398,978,571,53 is 1
Step 1: Since 978 > 398, we apply the division lemma to 978 and 398, to get
978 = 398 x 2 + 182
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 182 and 398, to get
398 = 182 x 2 + 34
Step 3: We consider the new divisor 182 and the new remainder 34, and apply the division lemma to get
182 = 34 x 5 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 398 and 978 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(182,34) = HCF(398,182) = HCF(978,398) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 571 > 2, we apply the division lemma to 571 and 2, to get
571 = 2 x 285 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 571 is 1
Notice that 1 = HCF(2,1) = HCF(571,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 53 > 1, we apply the division lemma to 53 and 1, to get
53 = 1 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 53 is 1
Notice that 1 = HCF(53,1) .
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Frequently Asked Questions on HCF of 398, 978, 571, 53 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 398, 978, 571, 53?
Answer: HCF of 398, 978, 571, 53 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 398, 978, 571, 53 using Euclid's Algorithm?
Answer: For arbitrary numbers 398, 978, 571, 53 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.