Highest Common Factor of 9712, 1904 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 9712, 1904 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 9712, 1904 is 16 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 9712, 1904 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 9712, 1904 is 16.
HCF(9712, 1904) = 16
HCF of 9712, 1904 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9712, 1904 is 16.
Highest Common Factor of 9712,1904 is 16
Step 1: Since 9712 > 1904, we apply the division lemma to 9712 and 1904, to get
9712 = 1904 x 5 + 192
Step 2: Since the reminder 1904 ≠ 0, we apply division lemma to 192 and 1904, to get
1904 = 192 x 9 + 176
Step 3: We consider the new divisor 192 and the new remainder 176, and apply the division lemma to get
192 = 176 x 1 + 16
We consider the new divisor 176 and the new remainder 16, and apply the division lemma to get
176 = 16 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 9712 and 1904 is 16
Notice that 16 = HCF(176,16) = HCF(192,176) = HCF(1904,192) = HCF(9712,1904) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9712, 1904 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 9712, 1904?
Answer: HCF of 9712, 1904 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9712, 1904 using Euclid's Algorithm?
Answer: For arbitrary numbers 9712, 1904 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
