Highest Common Factor of 675, 875 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 675, 875 i.e. 25 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 875 is 25 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 675, 875 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 675, 875 is 25.
HCF(675, 875) = 25
HCF of 675, 875 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 875 is 25.
Highest Common Factor of 675,875 is 25
Step 1: Since 875 > 675, we apply the division lemma to 875 and 675, to get
875 = 675 x 1 + 200
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 200 and 675, to get
675 = 200 x 3 + 75
Step 3: We consider the new divisor 200 and the new remainder 75, and apply the division lemma to get
200 = 75 x 2 + 50
We consider the new divisor 75 and the new remainder 50,and apply the division lemma to get
75 = 50 x 1 + 25
We consider the new divisor 50 and the new remainder 25,and apply the division lemma to get
50 = 25 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 675 and 875 is 25
Notice that 25 = HCF(50,25) = HCF(75,50) = HCF(200,75) = HCF(675,200) = HCF(875,675) .
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Frequently Asked Questions on HCF of 675, 875 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 675, 875?
Answer: HCF of 675, 875 is 25 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 875 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 875 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.