Highest Common Factor of 187, 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, 300 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 187, 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, 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, 300 is 1.
HCF(187, 300) = 1
HCF of 187, 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, 300 is 1.
Highest Common Factor of 187,300 is 1
Step 1: Since 300 > 187, we apply the division lemma to 300 and 187, to get
300 = 187 x 1 + 113
Step 2: Since the reminder 187 ≠ 0, we apply division lemma to 113 and 187, to get
187 = 113 x 1 + 74
Step 3: We consider the new divisor 113 and the new remainder 74, and apply the division lemma to get
113 = 74 x 1 + 39
We consider the new divisor 74 and the new remainder 39,and apply the division lemma to get
74 = 39 x 1 + 35
We consider the new divisor 39 and the new remainder 35,and apply the division lemma to get
39 = 35 x 1 + 4
We consider the new divisor 35 and the new remainder 4,and apply the division lemma to get
35 = 4 x 8 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 187 and 300 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(35,4) = HCF(39,35) = HCF(74,39) = HCF(113,74) = HCF(187,113) = HCF(300,187) .
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Frequently Asked Questions on HCF of 187, 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, 300?
Answer: HCF of 187, 300 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 187, 300 using Euclid's Algorithm?
Answer: For arbitrary numbers 187, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.