Highest Common Factor of 345, 230, 370 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, 230, 370 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 230, 370 is 5 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, 230, 370 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, 230, 370 is 5.
HCF(345, 230, 370) = 5
HCF of 345, 230, 370 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, 230, 370 is 5.
Highest Common Factor of 345,230,370 is 5
Step 1: Since 345 > 230, we apply the division lemma to 345 and 230, to get
345 = 230 x 1 + 115
Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 115 and 230, to get
230 = 115 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 115, the HCF of 345 and 230 is 115
Notice that 115 = HCF(230,115) = HCF(345,230) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 370 > 115, we apply the division lemma to 370 and 115, to get
370 = 115 x 3 + 25
Step 2: Since the reminder 115 ≠ 0, we apply division lemma to 25 and 115, to get
115 = 25 x 4 + 15
Step 3: We consider the new divisor 25 and the new remainder 15, and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 115 and 370 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(115,25) = HCF(370,115) .
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Frequently Asked Questions on HCF of 345, 230, 370 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, 230, 370?
Answer: HCF of 345, 230, 370 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 230, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 230, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.