Highest Common Factor of 1205, 3075 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 1205, 3075 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 1205, 3075 is 5 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 1205, 3075 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 1205, 3075 is 5.
HCF(1205, 3075) = 5
HCF of 1205, 3075 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1205, 3075 is 5.
Highest Common Factor of 1205,3075 is 5
Step 1: Since 3075 > 1205, we apply the division lemma to 3075 and 1205, to get
3075 = 1205 x 2 + 665
Step 2: Since the reminder 1205 ≠ 0, we apply division lemma to 665 and 1205, to get
1205 = 665 x 1 + 540
Step 3: We consider the new divisor 665 and the new remainder 540, and apply the division lemma to get
665 = 540 x 1 + 125
We consider the new divisor 540 and the new remainder 125,and apply the division lemma to get
540 = 125 x 4 + 40
We consider the new divisor 125 and the new remainder 40,and apply the division lemma to get
125 = 40 x 3 + 5
We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 1205 and 3075 is 5
Notice that 5 = HCF(40,5) = HCF(125,40) = HCF(540,125) = HCF(665,540) = HCF(1205,665) = HCF(3075,1205) .
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Frequently Asked Questions on HCF of 1205, 3075 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 1205, 3075?
Answer: HCF of 1205, 3075 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1205, 3075 using Euclid's Algorithm?
Answer: For arbitrary numbers 1205, 3075 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.