Highest Common Factor of 309, 5497 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 309, 5497 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 5497 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 309, 5497 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 309, 5497 is 1.
HCF(309, 5497) = 1
HCF of 309, 5497 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 5497 is 1.
Highest Common Factor of 309,5497 is 1
Step 1: Since 5497 > 309, we apply the division lemma to 5497 and 309, to get
5497 = 309 x 17 + 244
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 244 and 309, to get
309 = 244 x 1 + 65
Step 3: We consider the new divisor 244 and the new remainder 65, and apply the division lemma to get
244 = 65 x 3 + 49
We consider the new divisor 65 and the new remainder 49,and apply the division lemma to get
65 = 49 x 1 + 16
We consider the new divisor 49 and the new remainder 16,and apply the division lemma to get
49 = 16 x 3 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 309 and 5497 is 1
Notice that 1 = HCF(16,1) = HCF(49,16) = HCF(65,49) = HCF(244,65) = HCF(309,244) = HCF(5497,309) .
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Frequently Asked Questions on HCF of 309, 5497 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 309, 5497?
Answer: HCF of 309, 5497 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 5497 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 5497 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.