Highest Common Factor of 600, 375, 82 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 600, 375, 82 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 600, 375, 82 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 600, 375, 82 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 600, 375, 82 is 1.
HCF(600, 375, 82) = 1
HCF of 600, 375, 82 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 600, 375, 82 is 1.
Highest Common Factor of 600,375,82 is 1
Step 1: Since 600 > 375, we apply the division lemma to 600 and 375, to get
600 = 375 x 1 + 225
Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 225 and 375, to get
375 = 225 x 1 + 150
Step 3: We consider the new divisor 225 and the new remainder 150, and apply the division lemma to get
225 = 150 x 1 + 75
We consider the new divisor 150 and the new remainder 75, and apply the division lemma to get
150 = 75 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 600 and 375 is 75
Notice that 75 = HCF(150,75) = HCF(225,150) = HCF(375,225) = HCF(600,375) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82 > 75, we apply the division lemma to 82 and 75, to get
82 = 75 x 1 + 7
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 7 and 75, to get
75 = 7 x 10 + 5
Step 3: 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 75 and 82 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(75,7) = HCF(82,75) .
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Frequently Asked Questions on HCF of 600, 375, 82 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 600, 375, 82?
Answer: HCF of 600, 375, 82 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 600, 375, 82 using Euclid's Algorithm?
Answer: For arbitrary numbers 600, 375, 82 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.