Highest Common Factor of 478, 678, 503 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 478, 678, 503 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 478, 678, 503 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 478, 678, 503 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 478, 678, 503 is 1.
HCF(478, 678, 503) = 1
HCF of 478, 678, 503 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 478, 678, 503 is 1.
Highest Common Factor of 478,678,503 is 1
Step 1: Since 678 > 478, we apply the division lemma to 678 and 478, to get
678 = 478 x 1 + 200
Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 200 and 478, to get
478 = 200 x 2 + 78
Step 3: We consider the new divisor 200 and the new remainder 78, and apply the division lemma to get
200 = 78 x 2 + 44
We consider the new divisor 78 and the new remainder 44,and apply the division lemma to get
78 = 44 x 1 + 34
We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get
44 = 34 x 1 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 478 and 678 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(78,44) = HCF(200,78) = HCF(478,200) = HCF(678,478) .
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) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 478, 678, 503 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 478, 678, 503?
Answer: HCF of 478, 678, 503 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 478, 678, 503 using Euclid's Algorithm?
Answer: For arbitrary numbers 478, 678, 503 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.