Highest Common Factor of 504, 932, 814 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 504, 932, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 932, 814 is 2 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 504, 932, 814 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 504, 932, 814 is 2.
HCF(504, 932, 814) = 2
HCF of 504, 932, 814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 932, 814 is 2.
Highest Common Factor of 504,932,814 is 2
Step 1: Since 932 > 504, we apply the division lemma to 932 and 504, to get
932 = 504 x 1 + 428
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 428 and 504, to get
504 = 428 x 1 + 76
Step 3: We consider the new divisor 428 and the new remainder 76, and apply the division lemma to get
428 = 76 x 5 + 48
We consider the new divisor 76 and the new remainder 48,and apply the division lemma to get
76 = 48 x 1 + 28
We consider the new divisor 48 and the new remainder 28,and apply the division lemma to get
48 = 28 x 1 + 20
We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 504 and 932 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(48,28) = HCF(76,48) = HCF(428,76) = HCF(504,428) = HCF(932,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 4, we apply the division lemma to 814 and 4, to get
814 = 4 x 203 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 814 is 2
Notice that 2 = HCF(4,2) = HCF(814,4) .
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Frequently Asked Questions on HCF of 504, 932, 814 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 504, 932, 814?
Answer: HCF of 504, 932, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 932, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 932, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
