Highest Common Factor of 312, 192 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, 192 i.e. 24 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 192 is 24 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, 192 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, 192 is 24.
HCF(312, 192) = 24
HCF of 312, 192 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, 192 is 24.
Highest Common Factor of 312,192 is 24
Step 1: Since 312 > 192, we apply the division lemma to 312 and 192, to get
312 = 192 x 1 + 120
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 120 and 192, to get
192 = 120 x 1 + 72
Step 3: We consider the new divisor 120 and the new remainder 72, and apply the division lemma to get
120 = 72 x 1 + 48
We consider the new divisor 72 and the new remainder 48,and apply the division lemma to get
72 = 48 x 1 + 24
We consider the new divisor 48 and the new remainder 24,and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 312 and 192 is 24
Notice that 24 = HCF(48,24) = HCF(72,48) = HCF(120,72) = HCF(192,120) = HCF(312,192) .
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Frequently Asked Questions on HCF of 312, 192 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, 192?
Answer: HCF of 312, 192 is 24 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 192 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 192 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.