Highest Common Factor of 741, 8612, 2273 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 741, 8612, 2273 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 8612, 2273 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 741, 8612, 2273 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 741, 8612, 2273 is 1.
HCF(741, 8612, 2273) = 1
HCF of 741, 8612, 2273 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 741, 8612, 2273 is 1.
Highest Common Factor of 741,8612,2273 is 1
Step 1: Since 8612 > 741, we apply the division lemma to 8612 and 741, to get
8612 = 741 x 11 + 461
Step 2: Since the reminder 741 ≠ 0, we apply division lemma to 461 and 741, to get
741 = 461 x 1 + 280
Step 3: We consider the new divisor 461 and the new remainder 280, and apply the division lemma to get
461 = 280 x 1 + 181
We consider the new divisor 280 and the new remainder 181,and apply the division lemma to get
280 = 181 x 1 + 99
We consider the new divisor 181 and the new remainder 99,and apply the division lemma to get
181 = 99 x 1 + 82
We consider the new divisor 99 and the new remainder 82,and apply the division lemma to get
99 = 82 x 1 + 17
We consider the new divisor 82 and the new remainder 17,and apply the division lemma to get
82 = 17 x 4 + 14
We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get
17 = 14 x 1 + 3
We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get
14 = 3 x 4 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 741 and 8612 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(82,17) = HCF(99,82) = HCF(181,99) = HCF(280,181) = HCF(461,280) = HCF(741,461) = HCF(8612,741) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2273 > 1, we apply the division lemma to 2273 and 1, to get
2273 = 1 x 2273 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2273 is 1
Notice that 1 = HCF(2273,1) .
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Frequently Asked Questions on HCF of 741, 8612, 2273 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 741, 8612, 2273?
Answer: HCF of 741, 8612, 2273 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 8612, 2273 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 8612, 2273 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.