Highest Common Factor of 312, 800, 600 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 312, 800, 600 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 800, 600 is 8 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 312, 800, 600 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 312, 800, 600 is 8.
HCF(312, 800, 600) = 8
HCF of 312, 800, 600 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 800, 600 is 8.
Highest Common Factor of 312,800,600 is 8
Step 1: Since 800 > 312, we apply the division lemma to 800 and 312, to get
800 = 312 x 2 + 176
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 176 and 312, to get
312 = 176 x 1 + 136
Step 3: We consider the new divisor 176 and the new remainder 136, and apply the division lemma to get
176 = 136 x 1 + 40
We consider the new divisor 136 and the new remainder 40,and apply the division lemma to get
136 = 40 x 3 + 16
We consider the new divisor 40 and the new remainder 16,and apply the division lemma to get
40 = 16 x 2 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 312 and 800 is 8
Notice that 8 = HCF(16,8) = HCF(40,16) = HCF(136,40) = HCF(176,136) = HCF(312,176) = HCF(800,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 600 > 8, we apply the division lemma to 600 and 8, to get
600 = 8 x 75 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 600 is 8
Notice that 8 = HCF(600,8) .
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Frequently Asked Questions on HCF of 312, 800, 600 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 312, 800, 600?
Answer: HCF of 312, 800, 600 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 800, 600 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 800, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.