Highest Common Factor of 504, 306, 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, 306, 814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 306, 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, 306, 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, 306, 814 is 2.
HCF(504, 306, 814) = 2
HCF of 504, 306, 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, 306, 814 is 2.
Highest Common Factor of 504,306,814 is 2
Step 1: Since 504 > 306, we apply the division lemma to 504 and 306, to get
504 = 306 x 1 + 198
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 198 and 306, to get
306 = 198 x 1 + 108
Step 3: We consider the new divisor 198 and the new remainder 108, and apply the division lemma to get
198 = 108 x 1 + 90
We consider the new divisor 108 and the new remainder 90,and apply the division lemma to get
108 = 90 x 1 + 18
We consider the new divisor 90 and the new remainder 18,and apply the division lemma to get
90 = 18 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 504 and 306 is 18
Notice that 18 = HCF(90,18) = HCF(108,90) = HCF(198,108) = HCF(306,198) = HCF(504,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 814 > 18, we apply the division lemma to 814 and 18, to get
814 = 18 x 45 + 4
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 4 and 18, to get
18 = 4 x 4 + 2
Step 3: 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 18 and 814 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(814,18) .
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Frequently Asked Questions on HCF of 504, 306, 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, 306, 814?
Answer: HCF of 504, 306, 814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 306, 814 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 306, 814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.