Highest Common Factor of 195, 906 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, 906 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 195, 906 is 3 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, 906 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, 906 is 3.
HCF(195, 906) = 3
HCF of 195, 906 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, 906 is 3.
Highest Common Factor of 195,906 is 3
Step 1: Since 906 > 195, we apply the division lemma to 906 and 195, to get
906 = 195 x 4 + 126
Step 2: Since the reminder 195 ≠ 0, we apply division lemma to 126 and 195, to get
195 = 126 x 1 + 69
Step 3: We consider the new divisor 126 and the new remainder 69, and apply the division lemma to get
126 = 69 x 1 + 57
We consider the new divisor 69 and the new remainder 57,and apply the division lemma to get
69 = 57 x 1 + 12
We consider the new divisor 57 and the new remainder 12,and apply the division lemma to get
57 = 12 x 4 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 195 and 906 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(57,12) = HCF(69,57) = HCF(126,69) = HCF(195,126) = HCF(906,195) .
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Frequently Asked Questions on HCF of 195, 906 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, 906?
Answer: HCF of 195, 906 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 195, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 195, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.