Highest Common Factor of 780, 960, 513, 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 780, 960, 513, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 960, 513, 20 is 1 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 780, 960, 513, 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 780, 960, 513, 20 is 1.
HCF(780, 960, 513, 20) = 1
HCF of 780, 960, 513, 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 780, 960, 513, 20 is 1.
Highest Common Factor of 780,960,513,20 is 1
Step 1: Since 960 > 780, we apply the division lemma to 960 and 780, to get
960 = 780 x 1 + 180
Step 2: Since the reminder 780 ≠ 0, we apply division lemma to 180 and 780, to get
780 = 180 x 4 + 60
Step 3: We consider the new divisor 180 and the new remainder 60, and apply the division lemma to get
180 = 60 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 780 and 960 is 60
Notice that 60 = HCF(180,60) = HCF(780,180) = HCF(960,780) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 60, we apply the division lemma to 513 and 60, to get
513 = 60 x 8 + 33
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 33 and 60, to get
60 = 33 x 1 + 27
Step 3: We consider the new divisor 33 and the new remainder 27, and apply the division lemma to get
33 = 27 x 1 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 60 and 513 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(60,33) = HCF(513,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 3, we apply the division lemma to 20 and 3, to get
20 = 3 x 6 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 20 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) .
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Frequently Asked Questions on HCF of 780, 960, 513, 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 780, 960, 513, 20?
Answer: HCF of 780, 960, 513, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 960, 513, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 960, 513, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.