Highest Common Factor of 2075, 7475 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 2075, 7475 i.e. 25 the largest integer that leaves a remainder zero for all numbers.
HCF of 2075, 7475 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 2075, 7475 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 2075, 7475 is 25.
HCF(2075, 7475) = 25
HCF of 2075, 7475 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2075, 7475 is 25.
Highest Common Factor of 2075,7475 is 25
Step 1: Since 7475 > 2075, we apply the division lemma to 7475 and 2075, to get
7475 = 2075 x 3 + 1250
Step 2: Since the reminder 2075 ≠ 0, we apply division lemma to 1250 and 2075, to get
2075 = 1250 x 1 + 825
Step 3: We consider the new divisor 1250 and the new remainder 825, and apply the division lemma to get
1250 = 825 x 1 + 425
We consider the new divisor 825 and the new remainder 425,and apply the division lemma to get
825 = 425 x 1 + 400
We consider the new divisor 425 and the new remainder 400,and apply the division lemma to get
425 = 400 x 1 + 25
We consider the new divisor 400 and the new remainder 25,and apply the division lemma to get
400 = 25 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 2075 and 7475 is 25
Notice that 25 = HCF(400,25) = HCF(425,400) = HCF(825,425) = HCF(1250,825) = HCF(2075,1250) = HCF(7475,2075) .
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Frequently Asked Questions on HCF of 2075, 7475 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 2075, 7475?
Answer: HCF of 2075, 7475 is 25 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2075, 7475 using Euclid's Algorithm?
Answer: For arbitrary numbers 2075, 7475 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
