Highest Common Factor of 721, 427, 504 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 721, 427, 504 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 427, 504 is 7 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 721, 427, 504 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 721, 427, 504 is 7.
HCF(721, 427, 504) = 7
HCF of 721, 427, 504 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 427, 504 is 7.
Highest Common Factor of 721,427,504 is 7
Step 1: Since 721 > 427, we apply the division lemma to 721 and 427, to get
721 = 427 x 1 + 294
Step 2: Since the reminder 427 ≠ 0, we apply division lemma to 294 and 427, to get
427 = 294 x 1 + 133
Step 3: We consider the new divisor 294 and the new remainder 133, and apply the division lemma to get
294 = 133 x 2 + 28
We consider the new divisor 133 and the new remainder 28,and apply the division lemma to get
133 = 28 x 4 + 21
We consider the new divisor 28 and the new remainder 21,and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 721 and 427 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(133,28) = HCF(294,133) = HCF(427,294) = HCF(721,427) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 504 > 7, we apply the division lemma to 504 and 7, to get
504 = 7 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 504 is 7
Notice that 7 = HCF(504,7) .
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Frequently Asked Questions on HCF of 721, 427, 504 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 721, 427, 504?
Answer: HCF of 721, 427, 504 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 427, 504 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 427, 504 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.