Highest Common Factor of 1465, 905 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 1465, 905 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 1465, 905 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 1465, 905 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 1465, 905 is 5.
HCF(1465, 905) = 5
HCF of 1465, 905 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1465, 905 is 5.
Highest Common Factor of 1465,905 is 5
Step 1: Since 1465 > 905, we apply the division lemma to 1465 and 905, to get
1465 = 905 x 1 + 560
Step 2: Since the reminder 905 ≠ 0, we apply division lemma to 560 and 905, to get
905 = 560 x 1 + 345
Step 3: We consider the new divisor 560 and the new remainder 345, and apply the division lemma to get
560 = 345 x 1 + 215
We consider the new divisor 345 and the new remainder 215,and apply the division lemma to get
345 = 215 x 1 + 130
We consider the new divisor 215 and the new remainder 130,and apply the division lemma to get
215 = 130 x 1 + 85
We consider the new divisor 130 and the new remainder 85,and apply the division lemma to get
130 = 85 x 1 + 45
We consider the new divisor 85 and the new remainder 45,and apply the division lemma to get
85 = 45 x 1 + 40
We consider the new divisor 45 and the new remainder 40,and apply the division lemma to get
45 = 40 x 1 + 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 1465 and 905 is 5
Notice that 5 = HCF(40,5) = HCF(45,40) = HCF(85,45) = HCF(130,85) = HCF(215,130) = HCF(345,215) = HCF(560,345) = HCF(905,560) = HCF(1465,905) .
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Frequently Asked Questions on HCF of 1465, 905 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 1465, 905?
Answer: HCF of 1465, 905 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1465, 905 using Euclid's Algorithm?
Answer: For arbitrary numbers 1465, 905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.