Highest Common Factor of 728, 299 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 728, 299 i.e. 13 the largest integer that leaves a remainder zero for all numbers.
HCF of 728, 299 is 13 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 728, 299 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 728, 299 is 13.
HCF(728, 299) = 13
HCF of 728, 299 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 728, 299 is 13.
Highest Common Factor of 728,299 is 13
Step 1: Since 728 > 299, we apply the division lemma to 728 and 299, to get
728 = 299 x 2 + 130
Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 130 and 299, to get
299 = 130 x 2 + 39
Step 3: We consider the new divisor 130 and the new remainder 39, and apply the division lemma to get
130 = 39 x 3 + 13
We consider the new divisor 39 and the new remainder 13, and apply the division lemma to get
39 = 13 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 728 and 299 is 13
Notice that 13 = HCF(39,13) = HCF(130,39) = HCF(299,130) = HCF(728,299) .
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Frequently Asked Questions on HCF of 728, 299 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 728, 299?
Answer: HCF of 728, 299 is 13 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 728, 299 using Euclid's Algorithm?
Answer: For arbitrary numbers 728, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
