Highest Common Factor of 421, 728 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 421, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 728 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 421, 728 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 421, 728 is 1.
HCF(421, 728) = 1
HCF of 421, 728 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 421, 728 is 1.
Highest Common Factor of 421,728 is 1
Step 1: Since 728 > 421, we apply the division lemma to 728 and 421, to get
728 = 421 x 1 + 307
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 307 and 421, to get
421 = 307 x 1 + 114
Step 3: We consider the new divisor 307 and the new remainder 114, and apply the division lemma to get
307 = 114 x 2 + 79
We consider the new divisor 114 and the new remainder 79,and apply the division lemma to get
114 = 79 x 1 + 35
We consider the new divisor 79 and the new remainder 35,and apply the division lemma to get
79 = 35 x 2 + 9
We consider the new divisor 35 and the new remainder 9,and apply the division lemma to get
35 = 9 x 3 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 728 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(35,9) = HCF(79,35) = HCF(114,79) = HCF(307,114) = HCF(421,307) = HCF(728,421) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 421, 728 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 421, 728?
Answer: HCF of 421, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 728 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.