Highest Common Factor of 192, 909, 135 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 192, 909, 135 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 192, 909, 135 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 192, 909, 135 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 192, 909, 135 is 3.
HCF(192, 909, 135) = 3
HCF of 192, 909, 135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 192, 909, 135 is 3.
Highest Common Factor of 192,909,135 is 3
Step 1: Since 909 > 192, we apply the division lemma to 909 and 192, to get
909 = 192 x 4 + 141
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 141 and 192, to get
192 = 141 x 1 + 51
Step 3: We consider the new divisor 141 and the new remainder 51, and apply the division lemma to get
141 = 51 x 2 + 39
We consider the new divisor 51 and the new remainder 39,and apply the division lemma to get
51 = 39 x 1 + 12
We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get
39 = 12 x 3 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 192 and 909 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(141,51) = HCF(192,141) = HCF(909,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 135 > 3, we apply the division lemma to 135 and 3, to get
135 = 3 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 135 is 3
Notice that 3 = HCF(135,3) .
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Frequently Asked Questions on HCF of 192, 909, 135 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 192, 909, 135?
Answer: HCF of 192, 909, 135 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 192, 909, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 192, 909, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.