Highest Common Factor of 200, 277 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 200, 277 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 200, 277 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 200, 277 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 200, 277 is 1.
HCF(200, 277) = 1
HCF of 200, 277 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 200, 277 is 1.
Highest Common Factor of 200,277 is 1
Step 1: Since 277 > 200, we apply the division lemma to 277 and 200, to get
277 = 200 x 1 + 77
Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 77 and 200, to get
200 = 77 x 2 + 46
Step 3: We consider the new divisor 77 and the new remainder 46, and apply the division lemma to get
77 = 46 x 1 + 31
We consider the new divisor 46 and the new remainder 31,and apply the division lemma to get
46 = 31 x 1 + 15
We consider the new divisor 31 and the new remainder 15,and apply the division lemma to get
31 = 15 x 2 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 200 and 277 is 1
Notice that 1 = HCF(15,1) = HCF(31,15) = HCF(46,31) = HCF(77,46) = HCF(200,77) = HCF(277,200) .
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Frequently Asked Questions on HCF of 200, 277 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 200, 277?
Answer: HCF of 200, 277 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 200, 277 using Euclid's Algorithm?
Answer: For arbitrary numbers 200, 277 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.