Highest Common Factor of 258, 975 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 258, 975 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 258, 975 is 3 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 258, 975 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 258, 975 is 3.
HCF(258, 975) = 3
HCF of 258, 975 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 258, 975 is 3.
Highest Common Factor of 258,975 is 3
Step 1: Since 975 > 258, we apply the division lemma to 975 and 258, to get
975 = 258 x 3 + 201
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 201 and 258, to get
258 = 201 x 1 + 57
Step 3: We consider the new divisor 201 and the new remainder 57, and apply the division lemma to get
201 = 57 x 3 + 30
We consider the new divisor 57 and the new remainder 30,and apply the division lemma to get
57 = 30 x 1 + 27
We consider the new divisor 30 and the new remainder 27,and apply the division lemma to get
30 = 27 x 1 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 258 and 975 is 3
Notice that 3 = HCF(27,3) = HCF(30,27) = HCF(57,30) = HCF(201,57) = HCF(258,201) = HCF(975,258) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 258, 975 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 258, 975?
Answer: HCF of 258, 975 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 258, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 258, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.