Highest Common Factor of 721, 8603 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 721, 8603 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 8603 is 7 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 721, 8603 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 721, 8603 is 7.
HCF(721, 8603) = 7
HCF of 721, 8603 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 8603 is 7.
Highest Common Factor of 721,8603 is 7
Step 1: Since 8603 > 721, we apply the division lemma to 8603 and 721, to get
8603 = 721 x 11 + 672
Step 2: Since the reminder 721 ≠ 0, we apply division lemma to 672 and 721, to get
721 = 672 x 1 + 49
Step 3: We consider the new divisor 672 and the new remainder 49, and apply the division lemma to get
672 = 49 x 13 + 35
We consider the new divisor 49 and the new remainder 35,and apply the division lemma to get
49 = 35 x 1 + 14
We consider the new divisor 35 and the new remainder 14,and apply the division lemma to get
35 = 14 x 2 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 721 and 8603 is 7
Notice that 7 = HCF(14,7) = HCF(35,14) = HCF(49,35) = HCF(672,49) = HCF(721,672) = HCF(8603,721) .
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Frequently Asked Questions on HCF of 721, 8603 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 721, 8603?
Answer: HCF of 721, 8603 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 8603 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 8603 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
