Highest Common Factor of 780, 5769, 9987 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, 5769, 9987 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 5769, 9987 is 3 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, 5769, 9987 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, 5769, 9987 is 3.
HCF(780, 5769, 9987) = 3
HCF of 780, 5769, 9987 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, 5769, 9987 is 3.
Highest Common Factor of 780,5769,9987 is 3
Step 1: Since 5769 > 780, we apply the division lemma to 5769 and 780, to get
5769 = 780 x 7 + 309
Step 2: Since the reminder 780 ≠ 0, we apply division lemma to 309 and 780, to get
780 = 309 x 2 + 162
Step 3: We consider the new divisor 309 and the new remainder 162, and apply the division lemma to get
309 = 162 x 1 + 147
We consider the new divisor 162 and the new remainder 147,and apply the division lemma to get
162 = 147 x 1 + 15
We consider the new divisor 147 and the new remainder 15,and apply the division lemma to get
147 = 15 x 9 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 780 and 5769 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(147,15) = HCF(162,147) = HCF(309,162) = HCF(780,309) = HCF(5769,780) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9987 > 3, we apply the division lemma to 9987 and 3, to get
9987 = 3 x 3329 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 9987 is 3
Notice that 3 = HCF(9987,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 780, 5769, 9987 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, 5769, 9987?
Answer: HCF of 780, 5769, 9987 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 5769, 9987 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 5769, 9987 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.