Highest Common Factor of 177, 299 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 177, 299 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 177, 299 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 177, 299 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 177, 299 is 1.
HCF(177, 299) = 1
HCF of 177, 299 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 177, 299 is 1.
Highest Common Factor of 177,299 is 1
Step 1: Since 299 > 177, we apply the division lemma to 299 and 177, to get
299 = 177 x 1 + 122
Step 2: Since the reminder 177 ≠ 0, we apply division lemma to 122 and 177, to get
177 = 122 x 1 + 55
Step 3: We consider the new divisor 122 and the new remainder 55, and apply the division lemma to get
122 = 55 x 2 + 12
We consider the new divisor 55 and the new remainder 12,and apply the division lemma to get
55 = 12 x 4 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 177 and 299 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(55,12) = HCF(122,55) = HCF(177,122) = HCF(299,177) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 177, 299 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 177, 299?
Answer: HCF of 177, 299 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 177, 299 using Euclid's Algorithm?
Answer: For arbitrary numbers 177, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.