Highest Common Factor of 195, 320, 111 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 195, 320, 111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 195, 320, 111 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 195, 320, 111 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 195, 320, 111 is 1.
HCF(195, 320, 111) = 1
HCF of 195, 320, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 195, 320, 111 is 1.
Highest Common Factor of 195,320,111 is 1
Step 1: Since 320 > 195, we apply the division lemma to 320 and 195, to get
320 = 195 x 1 + 125
Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 125 and 195, to get
195 = 125 x 1 + 70
Step 3: We consider the new divisor 125 and the new remainder 70, and apply the division lemma to get
125 = 70 x 1 + 55
We consider the new divisor 70 and the new remainder 55,and apply the division lemma to get
70 = 55 x 1 + 15
We consider the new divisor 55 and the new remainder 15,and apply the division lemma to get
55 = 15 x 3 + 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 195 and 320 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) = HCF(70,55) = HCF(125,70) = HCF(195,125) = HCF(320,195) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 5, we apply the division lemma to 111 and 5, to get
111 = 5 x 22 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 111 is 1
Notice that 1 = HCF(5,1) = HCF(111,5) .
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Frequently Asked Questions on HCF of 195, 320, 111 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 195, 320, 111?
Answer: HCF of 195, 320, 111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 195, 320, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 195, 320, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.