Highest Common Factor of 312, 963, 105 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, 963, 105 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 963, 105 is 3 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, 963, 105 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, 963, 105 is 3.
HCF(312, 963, 105) = 3
HCF of 312, 963, 105 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, 963, 105 is 3.
Highest Common Factor of 312,963,105 is 3
Step 1: Since 963 > 312, we apply the division lemma to 963 and 312, to get
963 = 312 x 3 + 27
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 27 and 312, to get
312 = 27 x 11 + 15
Step 3: We consider the new divisor 27 and the new remainder 15, and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 312 and 963 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(312,27) = HCF(963,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 3, we apply the division lemma to 105 and 3, to get
105 = 3 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 105 is 3
Notice that 3 = HCF(105,3) .
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Frequently Asked Questions on HCF of 312, 963, 105 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, 963, 105?
Answer: HCF of 312, 963, 105 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 963, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 963, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.