Highest Common Factor of 9312, 3972 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 9312, 3972 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 9312, 3972 is 12 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 9312, 3972 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 9312, 3972 is 12.
HCF(9312, 3972) = 12
HCF of 9312, 3972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9312, 3972 is 12.
Highest Common Factor of 9312,3972 is 12
Step 1: Since 9312 > 3972, we apply the division lemma to 9312 and 3972, to get
9312 = 3972 x 2 + 1368
Step 2: Since the reminder 3972 ≠ 0, we apply division lemma to 1368 and 3972, to get
3972 = 1368 x 2 + 1236
Step 3: We consider the new divisor 1368 and the new remainder 1236, and apply the division lemma to get
1368 = 1236 x 1 + 132
We consider the new divisor 1236 and the new remainder 132,and apply the division lemma to get
1236 = 132 x 9 + 48
We consider the new divisor 132 and the new remainder 48,and apply the division lemma to get
132 = 48 x 2 + 36
We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get
48 = 36 x 1 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 9312 and 3972 is 12
Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(132,48) = HCF(1236,132) = HCF(1368,1236) = HCF(3972,1368) = HCF(9312,3972) .
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Frequently Asked Questions on HCF of 9312, 3972 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 9312, 3972?
Answer: HCF of 9312, 3972 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9312, 3972 using Euclid's Algorithm?
Answer: For arbitrary numbers 9312, 3972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.