Highest Common Factor of 442, 729, 905 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 442, 729, 905 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 442, 729, 905 is 1 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 442, 729, 905 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 442, 729, 905 is 1.
HCF(442, 729, 905) = 1
HCF of 442, 729, 905 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 442, 729, 905 is 1.
Highest Common Factor of 442,729,905 is 1
Step 1: Since 729 > 442, we apply the division lemma to 729 and 442, to get
729 = 442 x 1 + 287
Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 287 and 442, to get
442 = 287 x 1 + 155
Step 3: We consider the new divisor 287 and the new remainder 155, and apply the division lemma to get
287 = 155 x 1 + 132
We consider the new divisor 155 and the new remainder 132,and apply the division lemma to get
155 = 132 x 1 + 23
We consider the new divisor 132 and the new remainder 23,and apply the division lemma to get
132 = 23 x 5 + 17
We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get
23 = 17 x 1 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 442 and 729 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(132,23) = HCF(155,132) = HCF(287,155) = HCF(442,287) = HCF(729,442) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 905 > 1, we apply the division lemma to 905 and 1, to get
905 = 1 x 905 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 905 is 1
Notice that 1 = HCF(905,1) .
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Frequently Asked Questions on HCF of 442, 729, 905 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 442, 729, 905?
Answer: HCF of 442, 729, 905 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 442, 729, 905 using Euclid's Algorithm?
Answer: For arbitrary numbers 442, 729, 905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.