Highest Common Factor of 814, 308, 389, 305 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 814, 308, 389, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 814, 308, 389, 305 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 814, 308, 389, 305 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 814, 308, 389, 305 is 1.
HCF(814, 308, 389, 305) = 1
HCF of 814, 308, 389, 305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 814, 308, 389, 305 is 1.
Highest Common Factor of 814,308,389,305 is 1
Step 1: Since 814 > 308, we apply the division lemma to 814 and 308, to get
814 = 308 x 2 + 198
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 198 and 308, to get
308 = 198 x 1 + 110
Step 3: We consider the new divisor 198 and the new remainder 110, and apply the division lemma to get
198 = 110 x 1 + 88
We consider the new divisor 110 and the new remainder 88,and apply the division lemma to get
110 = 88 x 1 + 22
We consider the new divisor 88 and the new remainder 22,and apply the division lemma to get
88 = 22 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 814 and 308 is 22
Notice that 22 = HCF(88,22) = HCF(110,88) = HCF(198,110) = HCF(308,198) = HCF(814,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 389 > 22, we apply the division lemma to 389 and 22, to get
389 = 22 x 17 + 15
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 15 and 22, to get
22 = 15 x 1 + 7
Step 3: We consider the new divisor 15 and the new remainder 7, and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 22 and 389 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(389,22) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 305 > 1, we apply the division lemma to 305 and 1, to get
305 = 1 x 305 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 305 is 1
Notice that 1 = HCF(305,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 814, 308, 389, 305 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 814, 308, 389, 305?
Answer: HCF of 814, 308, 389, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 814, 308, 389, 305 using Euclid's Algorithm?
Answer: For arbitrary numbers 814, 308, 389, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.