Highest Common Factor of 84, 135, 177 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 84, 135, 177 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 84, 135, 177 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 84, 135, 177 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 84, 135, 177 is 3.
HCF(84, 135, 177) = 3
HCF of 84, 135, 177 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 84, 135, 177 is 3.
Highest Common Factor of 84,135,177 is 3
Step 1: Since 135 > 84, we apply the division lemma to 135 and 84, to get
135 = 84 x 1 + 51
Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 51 and 84, to get
84 = 51 x 1 + 33
Step 3: We consider the new divisor 51 and the new remainder 33, and apply the division lemma to get
51 = 33 x 1 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 84 and 135 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(84,51) = HCF(135,84) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 177 > 3, we apply the division lemma to 177 and 3, to get
177 = 3 x 59 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 177 is 3
Notice that 3 = HCF(177,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 84, 135, 177 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 84, 135, 177?
Answer: HCF of 84, 135, 177 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 84, 135, 177 using Euclid's Algorithm?
Answer: For arbitrary numbers 84, 135, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.