Highest Common Factor of 370, 230, 918 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 370, 230, 918 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 370, 230, 918 is 2 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 370, 230, 918 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 370, 230, 918 is 2.
HCF(370, 230, 918) = 2
HCF of 370, 230, 918 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 370, 230, 918 is 2.
Highest Common Factor of 370,230,918 is 2
Step 1: Since 370 > 230, we apply the division lemma to 370 and 230, to get
370 = 230 x 1 + 140
Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 140 and 230, to get
230 = 140 x 1 + 90
Step 3: We consider the new divisor 140 and the new remainder 90, and apply the division lemma to get
140 = 90 x 1 + 50
We consider the new divisor 90 and the new remainder 50,and apply the division lemma to get
90 = 50 x 1 + 40
We consider the new divisor 50 and the new remainder 40,and apply the division lemma to get
50 = 40 x 1 + 10
We consider the new divisor 40 and the new remainder 10,and apply the division lemma to get
40 = 10 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 370 and 230 is 10
Notice that 10 = HCF(40,10) = HCF(50,40) = HCF(90,50) = HCF(140,90) = HCF(230,140) = HCF(370,230) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 918 > 10, we apply the division lemma to 918 and 10, to get
918 = 10 x 91 + 8
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 8 and 10, to get
10 = 8 x 1 + 2
Step 3: We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 918 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(918,10) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 370, 230, 918 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 370, 230, 918?
Answer: HCF of 370, 230, 918 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 370, 230, 918 using Euclid's Algorithm?
Answer: For arbitrary numbers 370, 230, 918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.