Highest Common Factor of 200, 318, 100 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, 318, 100 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 200, 318, 100 is 2 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, 318, 100 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, 318, 100 is 2.
HCF(200, 318, 100) = 2
HCF of 200, 318, 100 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, 318, 100 is 2.
Highest Common Factor of 200,318,100 is 2
Step 1: Since 318 > 200, we apply the division lemma to 318 and 200, to get
318 = 200 x 1 + 118
Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 118 and 200, to get
200 = 118 x 1 + 82
Step 3: We consider the new divisor 118 and the new remainder 82, and apply the division lemma to get
118 = 82 x 1 + 36
We consider the new divisor 82 and the new remainder 36,and apply the division lemma to get
82 = 36 x 2 + 10
We consider the new divisor 36 and the new remainder 10,and apply the division lemma to get
36 = 10 x 3 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 200 and 318 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(82,36) = HCF(118,82) = HCF(200,118) = HCF(318,200) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 100 > 2, we apply the division lemma to 100 and 2, to get
100 = 2 x 50 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 100 is 2
Notice that 2 = HCF(100,2) .
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Frequently Asked Questions on HCF of 200, 318, 100 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, 318, 100?
Answer: HCF of 200, 318, 100 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 200, 318, 100 using Euclid's Algorithm?
Answer: For arbitrary numbers 200, 318, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.