Highest Common Factor of 971, 257 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 971, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 971, 257 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 971, 257 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 971, 257 is 1.
HCF(971, 257) = 1
HCF of 971, 257 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 971, 257 is 1.
Highest Common Factor of 971,257 is 1
Step 1: Since 971 > 257, we apply the division lemma to 971 and 257, to get
971 = 257 x 3 + 200
Step 2: Since the reminder 257 ≠ 0, we apply division lemma to 200 and 257, to get
257 = 200 x 1 + 57
Step 3: We consider the new divisor 200 and the new remainder 57, and apply the division lemma to get
200 = 57 x 3 + 29
We consider the new divisor 57 and the new remainder 29,and apply the division lemma to get
57 = 29 x 1 + 28
We consider the new divisor 29 and the new remainder 28,and apply the division lemma to get
29 = 28 x 1 + 1
We consider the new divisor 28 and the new remainder 1,and apply the division lemma to get
28 = 1 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 971 and 257 is 1
Notice that 1 = HCF(28,1) = HCF(29,28) = HCF(57,29) = HCF(200,57) = HCF(257,200) = HCF(971,257) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 971, 257 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 971, 257?
Answer: HCF of 971, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 971, 257 using Euclid's Algorithm?
Answer: For arbitrary numbers 971, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.