Highest Common Factor of 638, 978, 503, 682 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 638, 978, 503, 682 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 638, 978, 503, 682 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 638, 978, 503, 682 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 638, 978, 503, 682 is 1.
HCF(638, 978, 503, 682) = 1
HCF of 638, 978, 503, 682 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 638, 978, 503, 682 is 1.
Highest Common Factor of 638,978,503,682 is 1
Step 1: Since 978 > 638, we apply the division lemma to 978 and 638, to get
978 = 638 x 1 + 340
Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 340 and 638, to get
638 = 340 x 1 + 298
Step 3: We consider the new divisor 340 and the new remainder 298, and apply the division lemma to get
340 = 298 x 1 + 42
We consider the new divisor 298 and the new remainder 42,and apply the division lemma to get
298 = 42 x 7 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 638 and 978 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(298,42) = HCF(340,298) = HCF(638,340) = HCF(978,638) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 503 > 2, we apply the division lemma to 503 and 2, to get
503 = 2 x 251 + 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 503 is 1
Notice that 1 = HCF(2,1) = HCF(503,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 682 > 1, we apply the division lemma to 682 and 1, to get
682 = 1 x 682 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 682 is 1
Notice that 1 = HCF(682,1) .
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Frequently Asked Questions on HCF of 638, 978, 503, 682 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 638, 978, 503, 682?
Answer: HCF of 638, 978, 503, 682 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 638, 978, 503, 682 using Euclid's Algorithm?
Answer: For arbitrary numbers 638, 978, 503, 682 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.