Highest Common Factor of 135, 657, 141 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 135, 657, 141 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 135, 657, 141 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 135, 657, 141 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 135, 657, 141 is 3.
HCF(135, 657, 141) = 3
HCF of 135, 657, 141 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 135, 657, 141 is 3.
Highest Common Factor of 135,657,141 is 3
Step 1: Since 657 > 135, we apply the division lemma to 657 and 135, to get
657 = 135 x 4 + 117
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 117 and 135, to get
135 = 117 x 1 + 18
Step 3: We consider the new divisor 117 and the new remainder 18, and apply the division lemma to get
117 = 18 x 6 + 9
We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 135 and 657 is 9
Notice that 9 = HCF(18,9) = HCF(117,18) = HCF(135,117) = HCF(657,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 141 > 9, we apply the division lemma to 141 and 9, to get
141 = 9 x 15 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 141 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(141,9) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 135, 657, 141 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 135, 657, 141?
Answer: HCF of 135, 657, 141 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 135, 657, 141 using Euclid's Algorithm?
Answer: For arbitrary numbers 135, 657, 141 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.