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 516, 630, 682, 780 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 630, 682, 780 is 2 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 516, 630, 682, 780 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 516, 630, 682, 780 is 2.
HCF(516, 630, 682, 780) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 630, 682, 780 is 2.
Step 1: Since 630 > 516, we apply the division lemma to 630 and 516, to get
630 = 516 x 1 + 114
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 114 and 516, to get
516 = 114 x 4 + 60
Step 3: We consider the new divisor 114 and the new remainder 60, and apply the division lemma to get
114 = 60 x 1 + 54
We consider the new divisor 60 and the new remainder 54,and apply the division lemma to get
60 = 54 x 1 + 6
We consider the new divisor 54 and the new remainder 6,and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 516 and 630 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(114,60) = HCF(516,114) = HCF(630,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 682 > 6, we apply the division lemma to 682 and 6, to get
682 = 6 x 113 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 682 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(682,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 780 > 2, we apply the division lemma to 780 and 2, to get
780 = 2 x 390 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 780 is 2
Notice that 2 = HCF(780,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 516, 630, 682, 780?
Answer: HCF of 516, 630, 682, 780 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 630, 682, 780 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 630, 682, 780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.