Highest Common Factor of 764, 314, 966, 12 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 764, 314, 966, 12 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 764, 314, 966, 12 is 2 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 764, 314, 966, 12 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 764, 314, 966, 12 is 2.
HCF(764, 314, 966, 12) = 2
HCF of 764, 314, 966, 12 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 764, 314, 966, 12 is 2.
Highest Common Factor of 764,314,966,12 is 2
Step 1: Since 764 > 314, we apply the division lemma to 764 and 314, to get
764 = 314 x 2 + 136
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 136 and 314, to get
314 = 136 x 2 + 42
Step 3: We consider the new divisor 136 and the new remainder 42, and apply the division lemma to get
136 = 42 x 3 + 10
We consider the new divisor 42 and the new remainder 10,and apply the division lemma to get
42 = 10 x 4 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 764 and 314 is 2
Notice that 2 = HCF(10,2) = HCF(42,10) = HCF(136,42) = HCF(314,136) = HCF(764,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 966 > 2, we apply the division lemma to 966 and 2, to get
966 = 2 x 483 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 966 is 2
Notice that 2 = HCF(966,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12 > 2, we apply the division lemma to 12 and 2, to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 12 is 2
Notice that 2 = HCF(12,2) .
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Frequently Asked Questions on HCF of 764, 314, 966, 12 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 764, 314, 966, 12?
Answer: HCF of 764, 314, 966, 12 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 764, 314, 966, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 764, 314, 966, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.