Highest Common Factor of 345, 309, 31, 578 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 345, 309, 31, 578 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 309, 31, 578 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 345, 309, 31, 578 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 345, 309, 31, 578 is 1.
HCF(345, 309, 31, 578) = 1
HCF of 345, 309, 31, 578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 309, 31, 578 is 1.
Highest Common Factor of 345,309,31,578 is 1
Step 1: Since 345 > 309, we apply the division lemma to 345 and 309, to get
345 = 309 x 1 + 36
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 36 and 309, to get
309 = 36 x 8 + 21
Step 3: We consider the new divisor 36 and the new remainder 21, and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 345 and 309 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(309,36) = HCF(345,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 3, we apply the division lemma to 31 and 3, to get
31 = 3 x 10 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 31 is 1
Notice that 1 = HCF(3,1) = HCF(31,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 578 > 1, we apply the division lemma to 578 and 1, to get
578 = 1 x 578 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 578 is 1
Notice that 1 = HCF(578,1) .
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Frequently Asked Questions on HCF of 345, 309, 31, 578 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 345, 309, 31, 578?
Answer: HCF of 345, 309, 31, 578 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 309, 31, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 309, 31, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.