Highest Common Factor of 309, 473, 304, 25 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 309, 473, 304, 25 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 473, 304, 25 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 309, 473, 304, 25 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 309, 473, 304, 25 is 1.
HCF(309, 473, 304, 25) = 1
HCF of 309, 473, 304, 25 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 473, 304, 25 is 1.
Highest Common Factor of 309,473,304,25 is 1
Step 1: Since 473 > 309, we apply the division lemma to 473 and 309, to get
473 = 309 x 1 + 164
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 164 and 309, to get
309 = 164 x 1 + 145
Step 3: We consider the new divisor 164 and the new remainder 145, and apply the division lemma to get
164 = 145 x 1 + 19
We consider the new divisor 145 and the new remainder 19,and apply the division lemma to get
145 = 19 x 7 + 12
We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get
19 = 12 x 1 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 309 and 473 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(145,19) = HCF(164,145) = HCF(309,164) = HCF(473,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 304 > 1, we apply the division lemma to 304 and 1, to get
304 = 1 x 304 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 304 is 1
Notice that 1 = HCF(304,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 25 > 1, we apply the division lemma to 25 and 1, to get
25 = 1 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 25 is 1
Notice that 1 = HCF(25,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 309, 473, 304, 25 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 309, 473, 304, 25?
Answer: HCF of 309, 473, 304, 25 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 473, 304, 25 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 473, 304, 25 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.