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 9576, 1888, 14191 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9576, 1888, 14191 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 9576, 1888, 14191 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 9576, 1888, 14191 is 1.
HCF(9576, 1888, 14191) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9576, 1888, 14191 is 1.
Step 1: Since 9576 > 1888, we apply the division lemma to 9576 and 1888, to get
9576 = 1888 x 5 + 136
Step 2: Since the reminder 1888 ≠ 0, we apply division lemma to 136 and 1888, to get
1888 = 136 x 13 + 120
Step 3: We consider the new divisor 136 and the new remainder 120, and apply the division lemma to get
136 = 120 x 1 + 16
We consider the new divisor 120 and the new remainder 16,and apply the division lemma to get
120 = 16 x 7 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 9576 and 1888 is 8
Notice that 8 = HCF(16,8) = HCF(120,16) = HCF(136,120) = HCF(1888,136) = HCF(9576,1888) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14191 > 8, we apply the division lemma to 14191 and 8, to get
14191 = 8 x 1773 + 7
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 7 and 8, to get
8 = 7 x 1 + 1
Step 3: We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 14191 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(14191,8) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 9576, 1888, 14191?
Answer: HCF of 9576, 1888, 14191 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9576, 1888, 14191 using Euclid's Algorithm?
Answer: For arbitrary numbers 9576, 1888, 14191 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.