Highest Common Factor of 592, 960, 768 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 592, 960, 768 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 592, 960, 768 is 16 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 592, 960, 768 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 592, 960, 768 is 16.
HCF(592, 960, 768) = 16
HCF of 592, 960, 768 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 592, 960, 768 is 16.
Highest Common Factor of 592,960,768 is 16
Step 1: Since 960 > 592, we apply the division lemma to 960 and 592, to get
960 = 592 x 1 + 368
Step 2: Since the reminder 592 ≠ 0, we apply division lemma to 368 and 592, to get
592 = 368 x 1 + 224
Step 3: We consider the new divisor 368 and the new remainder 224, and apply the division lemma to get
368 = 224 x 1 + 144
We consider the new divisor 224 and the new remainder 144,and apply the division lemma to get
224 = 144 x 1 + 80
We consider the new divisor 144 and the new remainder 80,and apply the division lemma to get
144 = 80 x 1 + 64
We consider the new divisor 80 and the new remainder 64,and apply the division lemma to get
80 = 64 x 1 + 16
We consider the new divisor 64 and the new remainder 16,and apply the division lemma to get
64 = 16 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 592 and 960 is 16
Notice that 16 = HCF(64,16) = HCF(80,64) = HCF(144,80) = HCF(224,144) = HCF(368,224) = HCF(592,368) = HCF(960,592) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 768 > 16, we apply the division lemma to 768 and 16, to get
768 = 16 x 48 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 16 and 768 is 16
Notice that 16 = HCF(768,16) .
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Frequently Asked Questions on HCF of 592, 960, 768 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 592, 960, 768?
Answer: HCF of 592, 960, 768 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 592, 960, 768 using Euclid's Algorithm?
Answer: For arbitrary numbers 592, 960, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
