Highest Common Factor of 745, 7905 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, 7905 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 745, 7905 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, 7905 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, 7905 is 5.
HCF(745, 7905) = 5
HCF of 745, 7905 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, 7905 is 5.
Highest Common Factor of 745,7905 is 5
Step 1: Since 7905 > 745, we apply the division lemma to 7905 and 745, to get
7905 = 745 x 10 + 455
Step 2: Since the reminder 745 ≠ 0, we apply division lemma to 455 and 745, to get
745 = 455 x 1 + 290
Step 3: We consider the new divisor 455 and the new remainder 290, and apply the division lemma to get
455 = 290 x 1 + 165
We consider the new divisor 290 and the new remainder 165,and apply the division lemma to get
290 = 165 x 1 + 125
We consider the new divisor 165 and the new remainder 125,and apply the division lemma to get
165 = 125 x 1 + 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 745 and 7905 is 5
Notice that 5 = HCF(40,5) = HCF(125,40) = HCF(165,125) = HCF(290,165) = HCF(455,290) = HCF(745,455) = HCF(7905,745) .
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Frequently Asked Questions on HCF of 745, 7905 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, 7905?
Answer: HCF of 745, 7905 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 745, 7905 using Euclid's Algorithm?
Answer: For arbitrary numbers 745, 7905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.