Highest Common Factor of 306, 721 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 306, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 721 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 306, 721 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 306, 721 is 1.
HCF(306, 721) = 1
HCF of 306, 721 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 721 is 1.
Highest Common Factor of 306,721 is 1
Step 1: Since 721 > 306, we apply the division lemma to 721 and 306, to get
721 = 306 x 2 + 109
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 109 and 306, to get
306 = 109 x 2 + 88
Step 3: We consider the new divisor 109 and the new remainder 88, and apply the division lemma to get
109 = 88 x 1 + 21
We consider the new divisor 88 and the new remainder 21,and apply the division lemma to get
88 = 21 x 4 + 4
We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get
21 = 4 x 5 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 306 and 721 is 1
Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(88,21) = HCF(109,88) = HCF(306,109) = HCF(721,306) .
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Frequently Asked Questions on HCF of 306, 721 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 306, 721?
Answer: HCF of 306, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 721 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.