Highest Common Factor of 353, 8609 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 353, 8609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 353, 8609 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 353, 8609 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 353, 8609 is 1.
HCF(353, 8609) = 1
HCF of 353, 8609 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 353, 8609 is 1.
Highest Common Factor of 353,8609 is 1
Step 1: Since 8609 > 353, we apply the division lemma to 8609 and 353, to get
8609 = 353 x 24 + 137
Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 137 and 353, to get
353 = 137 x 2 + 79
Step 3: We consider the new divisor 137 and the new remainder 79, and apply the division lemma to get
137 = 79 x 1 + 58
We consider the new divisor 79 and the new remainder 58,and apply the division lemma to get
79 = 58 x 1 + 21
We consider the new divisor 58 and the new remainder 21,and apply the division lemma to get
58 = 21 x 2 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 353 and 8609 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(58,21) = HCF(79,58) = HCF(137,79) = HCF(353,137) = HCF(8609,353) .
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Frequently Asked Questions on HCF of 353, 8609 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 353, 8609?
Answer: HCF of 353, 8609 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 353, 8609 using Euclid's Algorithm?
Answer: For arbitrary numbers 353, 8609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
