Highest Common Factor of 9906, 1725 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 9906, 1725 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9906, 1725 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 9906, 1725 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 9906, 1725 is 3.
HCF(9906, 1725) = 3
HCF of 9906, 1725 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9906, 1725 is 3.
Highest Common Factor of 9906,1725 is 3
Step 1: Since 9906 > 1725, we apply the division lemma to 9906 and 1725, to get
9906 = 1725 x 5 + 1281
Step 2: Since the reminder 1725 ≠ 0, we apply division lemma to 1281 and 1725, to get
1725 = 1281 x 1 + 444
Step 3: We consider the new divisor 1281 and the new remainder 444, and apply the division lemma to get
1281 = 444 x 2 + 393
We consider the new divisor 444 and the new remainder 393,and apply the division lemma to get
444 = 393 x 1 + 51
We consider the new divisor 393 and the new remainder 51,and apply the division lemma to get
393 = 51 x 7 + 36
We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get
51 = 36 x 1 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9906 and 1725 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(393,51) = HCF(444,393) = HCF(1281,444) = HCF(1725,1281) = HCF(9906,1725) .
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Frequently Asked Questions on HCF of 9906, 1725 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 9906, 1725?
Answer: HCF of 9906, 1725 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9906, 1725 using Euclid's Algorithm?
Answer: For arbitrary numbers 9906, 1725 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.