Highest Common Factor of 9905, 1602 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 9905, 1602 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9905, 1602 is 1 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 9905, 1602 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 9905, 1602 is 1.
HCF(9905, 1602) = 1
HCF of 9905, 1602 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9905, 1602 is 1.
Highest Common Factor of 9905,1602 is 1
Step 1: Since 9905 > 1602, we apply the division lemma to 9905 and 1602, to get
9905 = 1602 x 6 + 293
Step 2: Since the reminder 1602 ≠ 0, we apply division lemma to 293 and 1602, to get
1602 = 293 x 5 + 137
Step 3: We consider the new divisor 293 and the new remainder 137, and apply the division lemma to get
293 = 137 x 2 + 19
We consider the new divisor 137 and the new remainder 19,and apply the division lemma to get
137 = 19 x 7 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9905 and 1602 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(137,19) = HCF(293,137) = HCF(1602,293) = HCF(9905,1602) .
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Frequently Asked Questions on HCF of 9905, 1602 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 9905, 1602?
Answer: HCF of 9905, 1602 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9905, 1602 using Euclid's Algorithm?
Answer: For arbitrary numbers 9905, 1602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.