Highest Common Factor of 9738, 2272 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 9738, 2272 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9738, 2272 is 2 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 9738, 2272 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 9738, 2272 is 2.
HCF(9738, 2272) = 2
HCF of 9738, 2272 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9738, 2272 is 2.
Highest Common Factor of 9738,2272 is 2
Step 1: Since 9738 > 2272, we apply the division lemma to 9738 and 2272, to get
9738 = 2272 x 4 + 650
Step 2: Since the reminder 2272 ≠ 0, we apply division lemma to 650 and 2272, to get
2272 = 650 x 3 + 322
Step 3: We consider the new divisor 650 and the new remainder 322, and apply the division lemma to get
650 = 322 x 2 + 6
We consider the new divisor 322 and the new remainder 6,and apply the division lemma to get
322 = 6 x 53 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9738 and 2272 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(322,6) = HCF(650,322) = HCF(2272,650) = HCF(9738,2272) .
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Frequently Asked Questions on HCF of 9738, 2272 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 9738, 2272?
Answer: HCF of 9738, 2272 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9738, 2272 using Euclid's Algorithm?
Answer: For arbitrary numbers 9738, 2272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.