Highest Common Factor of 9690, 903 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 9690, 903 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9690, 903 is 3 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 9690, 903 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 9690, 903 is 3.
HCF(9690, 903) = 3
HCF of 9690, 903 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9690, 903 is 3.
Highest Common Factor of 9690,903 is 3
Step 1: Since 9690 > 903, we apply the division lemma to 9690 and 903, to get
9690 = 903 x 10 + 660
Step 2: Since the reminder 903 ≠ 0, we apply division lemma to 660 and 903, to get
903 = 660 x 1 + 243
Step 3: We consider the new divisor 660 and the new remainder 243, and apply the division lemma to get
660 = 243 x 2 + 174
We consider the new divisor 243 and the new remainder 174,and apply the division lemma to get
243 = 174 x 1 + 69
We consider the new divisor 174 and the new remainder 69,and apply the division lemma to get
174 = 69 x 2 + 36
We consider the new divisor 69 and the new remainder 36,and apply the division lemma to get
69 = 36 x 1 + 33
We consider the new divisor 36 and the new remainder 33,and apply the division lemma to get
36 = 33 x 1 + 3
We consider the new divisor 33 and the new remainder 3,and apply the division lemma to get
33 = 3 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9690 and 903 is 3
Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(69,36) = HCF(174,69) = HCF(243,174) = HCF(660,243) = HCF(903,660) = HCF(9690,903) .
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Frequently Asked Questions on HCF of 9690, 903 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 9690, 903?
Answer: HCF of 9690, 903 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9690, 903 using Euclid's Algorithm?
Answer: For arbitrary numbers 9690, 903 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.