Highest Common Factor of 897, 1455, 1721 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 897, 1455, 1721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 897, 1455, 1721 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 897, 1455, 1721 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 897, 1455, 1721 is 1.
HCF(897, 1455, 1721) = 1
HCF of 897, 1455, 1721 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 897, 1455, 1721 is 1.
Highest Common Factor of 897,1455,1721 is 1
Step 1: Since 1455 > 897, we apply the division lemma to 1455 and 897, to get
1455 = 897 x 1 + 558
Step 2: Since the reminder 897 ≠ 0, we apply division lemma to 558 and 897, to get
897 = 558 x 1 + 339
Step 3: We consider the new divisor 558 and the new remainder 339, and apply the division lemma to get
558 = 339 x 1 + 219
We consider the new divisor 339 and the new remainder 219,and apply the division lemma to get
339 = 219 x 1 + 120
We consider the new divisor 219 and the new remainder 120,and apply the division lemma to get
219 = 120 x 1 + 99
We consider the new divisor 120 and the new remainder 99,and apply the division lemma to get
120 = 99 x 1 + 21
We consider the new divisor 99 and the new remainder 21,and apply the division lemma to get
99 = 21 x 4 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 897 and 1455 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(99,21) = HCF(120,99) = HCF(219,120) = HCF(339,219) = HCF(558,339) = HCF(897,558) = HCF(1455,897) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1721 > 3, we apply the division lemma to 1721 and 3, to get
1721 = 3 x 573 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 1721 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(1721,3) .
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Frequently Asked Questions on HCF of 897, 1455, 1721 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 897, 1455, 1721?
Answer: HCF of 897, 1455, 1721 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 897, 1455, 1721 using Euclid's Algorithm?
Answer: For arbitrary numbers 897, 1455, 1721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.