Highest Common Factor of 187, 353, 300 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 187, 353, 300 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 187, 353, 300 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 187, 353, 300 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 187, 353, 300 is 1.
HCF(187, 353, 300) = 1
HCF of 187, 353, 300 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 187, 353, 300 is 1.
Highest Common Factor of 187,353,300 is 1
Step 1: Since 353 > 187, we apply the division lemma to 353 and 187, to get
353 = 187 x 1 + 166
Step 2: Since the reminder 187 ≠ 0, we apply division lemma to 166 and 187, to get
187 = 166 x 1 + 21
Step 3: We consider the new divisor 166 and the new remainder 21, and apply the division lemma to get
166 = 21 x 7 + 19
We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get
21 = 19 x 1 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 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 187 and 353 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(166,21) = HCF(187,166) = HCF(353,187) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 300 > 1, we apply the division lemma to 300 and 1, to get
300 = 1 x 300 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 300 is 1
Notice that 1 = HCF(300,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 187, 353, 300 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 187, 353, 300?
Answer: HCF of 187, 353, 300 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 187, 353, 300 using Euclid's Algorithm?
Answer: For arbitrary numbers 187, 353, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.