Highest Common Factor of 384, 528, 76 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 384, 528, 76 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 384, 528, 76 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 384, 528, 76 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 384, 528, 76 is 4.
HCF(384, 528, 76) = 4
HCF of 384, 528, 76 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 384, 528, 76 is 4.
Highest Common Factor of 384,528,76 is 4
Step 1: Since 528 > 384, we apply the division lemma to 528 and 384, to get
528 = 384 x 1 + 144
Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 144 and 384, to get
384 = 144 x 2 + 96
Step 3: We consider the new divisor 144 and the new remainder 96, and apply the division lemma to get
144 = 96 x 1 + 48
We consider the new divisor 96 and the new remainder 48, and apply the division lemma to get
96 = 48 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 384 and 528 is 48
Notice that 48 = HCF(96,48) = HCF(144,96) = HCF(384,144) = HCF(528,384) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 76 > 48, we apply the division lemma to 76 and 48, to get
76 = 48 x 1 + 28
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 28 and 48, to get
48 = 28 x 1 + 20
Step 3: We consider the new divisor 28 and the new remainder 20, and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 48 and 76 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(48,28) = HCF(76,48) .
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Frequently Asked Questions on HCF of 384, 528, 76 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 384, 528, 76?
Answer: HCF of 384, 528, 76 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 384, 528, 76 using Euclid's Algorithm?
Answer: For arbitrary numbers 384, 528, 76 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.