Highest Common Factor of 784, 960, 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 784, 960, 12 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 960, 12 is 4 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 784, 960, 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 784, 960, 12 is 4.
HCF(784, 960, 12) = 4
HCF of 784, 960, 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 784, 960, 12 is 4.
Highest Common Factor of 784,960,12 is 4
Step 1: Since 960 > 784, we apply the division lemma to 960 and 784, to get
960 = 784 x 1 + 176
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 176 and 784, to get
784 = 176 x 4 + 80
Step 3: We consider the new divisor 176 and the new remainder 80, and apply the division lemma to get
176 = 80 x 2 + 16
We consider the new divisor 80 and the new remainder 16, and apply the division lemma to get
80 = 16 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 784 and 960 is 16
Notice that 16 = HCF(80,16) = HCF(176,80) = HCF(784,176) = HCF(960,784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 12, we apply the division lemma to 16 and 12, to get
16 = 12 x 1 + 4
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 4 and 12, to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 16 and 12 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) .
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Frequently Asked Questions on HCF of 784, 960, 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 784, 960, 12?
Answer: HCF of 784, 960, 12 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 960, 12 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 960, 12 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.