Highest Common Factor of 745, 75115 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 745, 75115 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 745, 75115 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 745, 75115 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 745, 75115 is 5.
HCF(745, 75115) = 5
HCF of 745, 75115 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 745, 75115 is 5.
Highest Common Factor of 745,75115 is 5
Step 1: Since 75115 > 745, we apply the division lemma to 75115 and 745, to get
75115 = 745 x 100 + 615
Step 2: Since the reminder 745 ≠ 0, we apply division lemma to 615 and 745, to get
745 = 615 x 1 + 130
Step 3: We consider the new divisor 615 and the new remainder 130, and apply the division lemma to get
615 = 130 x 4 + 95
We consider the new divisor 130 and the new remainder 95,and apply the division lemma to get
130 = 95 x 1 + 35
We consider the new divisor 95 and the new remainder 35,and apply the division lemma to get
95 = 35 x 2 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 745 and 75115 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(95,35) = HCF(130,95) = HCF(615,130) = HCF(745,615) = HCF(75115,745) .
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Frequently Asked Questions on HCF of 745, 75115 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 745, 75115?
Answer: HCF of 745, 75115 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 745, 75115 using Euclid's Algorithm?
Answer: For arbitrary numbers 745, 75115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.