Highest Common Factor of 297, 9680 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 297, 9680 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 297, 9680 is 11 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 297, 9680 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 297, 9680 is 11.
HCF(297, 9680) = 11
HCF of 297, 9680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 297, 9680 is 11.
Highest Common Factor of 297,9680 is 11
Step 1: Since 9680 > 297, we apply the division lemma to 9680 and 297, to get
9680 = 297 x 32 + 176
Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 176 and 297, to get
297 = 176 x 1 + 121
Step 3: We consider the new divisor 176 and the new remainder 121, and apply the division lemma to get
176 = 121 x 1 + 55
We consider the new divisor 121 and the new remainder 55,and apply the division lemma to get
121 = 55 x 2 + 11
We consider the new divisor 55 and the new remainder 11,and apply the division lemma to get
55 = 11 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 297 and 9680 is 11
Notice that 11 = HCF(55,11) = HCF(121,55) = HCF(176,121) = HCF(297,176) = HCF(9680,297) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 297, 9680 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 297, 9680?
Answer: HCF of 297, 9680 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 297, 9680 using Euclid's Algorithm?
Answer: For arbitrary numbers 297, 9680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.