Highest Common Factor of 1540, 9609 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 1540, 9609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1540, 9609 is 1 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 1540, 9609 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 1540, 9609 is 1.
HCF(1540, 9609) = 1
HCF of 1540, 9609 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1540, 9609 is 1.
Highest Common Factor of 1540,9609 is 1
Step 1: Since 9609 > 1540, we apply the division lemma to 9609 and 1540, to get
9609 = 1540 x 6 + 369
Step 2: Since the reminder 1540 ≠ 0, we apply division lemma to 369 and 1540, to get
1540 = 369 x 4 + 64
Step 3: We consider the new divisor 369 and the new remainder 64, and apply the division lemma to get
369 = 64 x 5 + 49
We consider the new divisor 64 and the new remainder 49,and apply the division lemma to get
64 = 49 x 1 + 15
We consider the new divisor 49 and the new remainder 15,and apply the division lemma to get
49 = 15 x 3 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1540 and 9609 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(49,15) = HCF(64,49) = HCF(369,64) = HCF(1540,369) = HCF(9609,1540) .
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Frequently Asked Questions on HCF of 1540, 9609 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 1540, 9609?
Answer: HCF of 1540, 9609 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1540, 9609 using Euclid's Algorithm?
Answer: For arbitrary numbers 1540, 9609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.