Highest Common Factor of 421, 308 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, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 308 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, 308 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, 308 is 1.
HCF(421, 308) = 1
HCF of 421, 308 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, 308 is 1.
Highest Common Factor of 421,308 is 1
Step 1: Since 421 > 308, we apply the division lemma to 421 and 308, to get
421 = 308 x 1 + 113
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 113 and 308, to get
308 = 113 x 2 + 82
Step 3: We consider the new divisor 113 and the new remainder 82, and apply the division lemma to get
113 = 82 x 1 + 31
We consider the new divisor 82 and the new remainder 31,and apply the division lemma to get
82 = 31 x 2 + 20
We consider the new divisor 31 and the new remainder 20,and apply the division lemma to get
31 = 20 x 1 + 11
We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 308 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(82,31) = HCF(113,82) = HCF(308,113) = HCF(421,308) .
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Frequently Asked Questions on HCF of 421, 308 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, 308?
Answer: HCF of 421, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
