Highest Common Factor of 257, 45897 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 257, 45897 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 257, 45897 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 257, 45897 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 257, 45897 is 1.
HCF(257, 45897) = 1
HCF of 257, 45897 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 257, 45897 is 1.
Highest Common Factor of 257,45897 is 1
Step 1: Since 45897 > 257, we apply the division lemma to 45897 and 257, to get
45897 = 257 x 178 + 151
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 151 and 257, to get
257 = 151 x 1 + 106
Step 3: We consider the new divisor 151 and the new remainder 106, and apply the division lemma to get
151 = 106 x 1 + 45
We consider the new divisor 106 and the new remainder 45,and apply the division lemma to get
106 = 45 x 2 + 16
We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get
45 = 16 x 2 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 257 and 45897 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(106,45) = HCF(151,106) = HCF(257,151) = HCF(45897,257) .
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Frequently Asked Questions on HCF of 257, 45897 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 257, 45897?
Answer: HCF of 257, 45897 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 257, 45897 using Euclid's Algorithm?
Answer: For arbitrary numbers 257, 45897 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
