Highest Common Factor of 792, 512, 20 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 792, 512, 20 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 792, 512, 20 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 792, 512, 20 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 792, 512, 20 is 4.
HCF(792, 512, 20) = 4
HCF of 792, 512, 20 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 792, 512, 20 is 4.
Highest Common Factor of 792,512,20 is 4
Step 1: Since 792 > 512, we apply the division lemma to 792 and 512, to get
792 = 512 x 1 + 280
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 280 and 512, to get
512 = 280 x 1 + 232
Step 3: We consider the new divisor 280 and the new remainder 232, and apply the division lemma to get
280 = 232 x 1 + 48
We consider the new divisor 232 and the new remainder 48,and apply the division lemma to get
232 = 48 x 4 + 40
We consider the new divisor 48 and the new remainder 40,and apply the division lemma to get
48 = 40 x 1 + 8
We consider the new divisor 40 and the new remainder 8,and apply the division lemma to get
40 = 8 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 792 and 512 is 8
Notice that 8 = HCF(40,8) = HCF(48,40) = HCF(232,48) = HCF(280,232) = HCF(512,280) = HCF(792,512) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 8, we apply the division lemma to 20 and 8, to get
20 = 8 x 2 + 4
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, 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 8 and 20 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) .
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Frequently Asked Questions on HCF of 792, 512, 20 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 792, 512, 20?
Answer: HCF of 792, 512, 20 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 792, 512, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 792, 512, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.