Highest Common Factor of 9735, 3121, 11150 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 9735, 3121, 11150 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9735, 3121, 11150 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 9735, 3121, 11150 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 9735, 3121, 11150 is 1.
HCF(9735, 3121, 11150) = 1
HCF of 9735, 3121, 11150 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9735, 3121, 11150 is 1.
Highest Common Factor of 9735,3121,11150 is 1
Step 1: Since 9735 > 3121, we apply the division lemma to 9735 and 3121, to get
9735 = 3121 x 3 + 372
Step 2: Since the reminder 3121 ≠ 0, we apply division lemma to 372 and 3121, to get
3121 = 372 x 8 + 145
Step 3: We consider the new divisor 372 and the new remainder 145, and apply the division lemma to get
372 = 145 x 2 + 82
We consider the new divisor 145 and the new remainder 82,and apply the division lemma to get
145 = 82 x 1 + 63
We consider the new divisor 82 and the new remainder 63,and apply the division lemma to get
82 = 63 x 1 + 19
We consider the new divisor 63 and the new remainder 19,and apply the division lemma to get
63 = 19 x 3 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9735 and 3121 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(63,19) = HCF(82,63) = HCF(145,82) = HCF(372,145) = HCF(3121,372) = HCF(9735,3121) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 11150 > 1, we apply the division lemma to 11150 and 1, to get
11150 = 1 x 11150 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11150 is 1
Notice that 1 = HCF(11150,1) .
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Frequently Asked Questions on HCF of 9735, 3121, 11150 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 9735, 3121, 11150?
Answer: HCF of 9735, 3121, 11150 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9735, 3121, 11150 using Euclid's Algorithm?
Answer: For arbitrary numbers 9735, 3121, 11150 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
