Highest Common Factor of 504, 7418 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, 7418 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 7418 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, 7418 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, 7418 is 2.
HCF(504, 7418) = 2
HCF of 504, 7418 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, 7418 is 2.
Highest Common Factor of 504,7418 is 2
Step 1: Since 7418 > 504, we apply the division lemma to 7418 and 504, to get
7418 = 504 x 14 + 362
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 362 and 504, to get
504 = 362 x 1 + 142
Step 3: We consider the new divisor 362 and the new remainder 142, and apply the division lemma to get
362 = 142 x 2 + 78
We consider the new divisor 142 and the new remainder 78,and apply the division lemma to get
142 = 78 x 1 + 64
We consider the new divisor 78 and the new remainder 64,and apply the division lemma to get
78 = 64 x 1 + 14
We consider the new divisor 64 and the new remainder 14,and apply the division lemma to get
64 = 14 x 4 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 504 and 7418 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(64,14) = HCF(78,64) = HCF(142,78) = HCF(362,142) = HCF(504,362) = HCF(7418,504) .
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Frequently Asked Questions on HCF of 504, 7418 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, 7418?
Answer: HCF of 504, 7418 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 7418 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 7418 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.