Highest Common Factor of 870, 516, 468 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 870, 516, 468 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 516, 468 is 6 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 870, 516, 468 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 870, 516, 468 is 6.
HCF(870, 516, 468) = 6
HCF of 870, 516, 468 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 516, 468 is 6.
Highest Common Factor of 870,516,468 is 6
Step 1: Since 870 > 516, we apply the division lemma to 870 and 516, to get
870 = 516 x 1 + 354
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 354 and 516, to get
516 = 354 x 1 + 162
Step 3: We consider the new divisor 354 and the new remainder 162, and apply the division lemma to get
354 = 162 x 2 + 30
We consider the new divisor 162 and the new remainder 30,and apply the division lemma to get
162 = 30 x 5 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 870 and 516 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(162,30) = HCF(354,162) = HCF(516,354) = HCF(870,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 468 > 6, we apply the division lemma to 468 and 6, to get
468 = 6 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 468 is 6
Notice that 6 = HCF(468,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 870, 516, 468 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 870, 516, 468?
Answer: HCF of 870, 516, 468 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 516, 468 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 516, 468 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.