Highest Common Factor of 721, 441, 497 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, 441, 497 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 441, 497 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, 441, 497 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, 441, 497 is 7.
HCF(721, 441, 497) = 7
HCF of 721, 441, 497 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, 441, 497 is 7.
Highest Common Factor of 721,441,497 is 7
Step 1: Since 721 > 441, we apply the division lemma to 721 and 441, to get
721 = 441 x 1 + 280
Step 2: Since the reminder 441 ≠ 0, we apply division lemma to 280 and 441, to get
441 = 280 x 1 + 161
Step 3: We consider the new divisor 280 and the new remainder 161, and apply the division lemma to get
280 = 161 x 1 + 119
We consider the new divisor 161 and the new remainder 119,and apply the division lemma to get
161 = 119 x 1 + 42
We consider the new divisor 119 and the new remainder 42,and apply the division lemma to get
119 = 42 x 2 + 35
We consider the new divisor 42 and the new remainder 35,and apply the division lemma to get
42 = 35 x 1 + 7
We consider the new divisor 35 and the new remainder 7,and apply the division lemma to get
35 = 7 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 721 and 441 is 7
Notice that 7 = HCF(35,7) = HCF(42,35) = HCF(119,42) = HCF(161,119) = HCF(280,161) = HCF(441,280) = HCF(721,441) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 497 > 7, we apply the division lemma to 497 and 7, to get
497 = 7 x 71 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 497 is 7
Notice that 7 = HCF(497,7) .
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Frequently Asked Questions on HCF of 721, 441, 497 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, 441, 497?
Answer: HCF of 721, 441, 497 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 441, 497 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 441, 497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
