Highest Common Factor of 172, 989, 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 172, 989, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 989, 177 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 172, 989, 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 172, 989, 177 is 1.
HCF(172, 989, 177) = 1
HCF of 172, 989, 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 172, 989, 177 is 1.
Highest Common Factor of 172,989,177 is 1
Step 1: Since 989 > 172, we apply the division lemma to 989 and 172, to get
989 = 172 x 5 + 129
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 129 and 172, to get
172 = 129 x 1 + 43
Step 3: We consider the new divisor 129 and the new remainder 43, and apply the division lemma to get
129 = 43 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 172 and 989 is 43
Notice that 43 = HCF(129,43) = HCF(172,129) = HCF(989,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 177 > 43, we apply the division lemma to 177 and 43, to get
177 = 43 x 4 + 5
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 5 and 43, to get
43 = 5 x 8 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 177 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(43,5) = HCF(177,43) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 172, 989, 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 172, 989, 177?
Answer: HCF of 172, 989, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 989, 177 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 989, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
