Highest Common Factor of 516, 990, 90 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 516, 990, 90 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 990, 90 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 516, 990, 90 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, 990, 90 is 6.
HCF(516, 990, 90) = 6
HCF of 516, 990, 90 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 990, 90 is 6.
Highest Common Factor of 516,990,90 is 6
Step 1: Since 990 > 516, we apply the division lemma to 990 and 516, to get
990 = 516 x 1 + 474
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 474 and 516, to get
516 = 474 x 1 + 42
Step 3: We consider the new divisor 474 and the new remainder 42, and apply the division lemma to get
474 = 42 x 11 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 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 516 and 990 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(474,42) = HCF(516,474) = HCF(990,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 90 > 6, we apply the division lemma to 90 and 6, to get
90 = 6 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 90 is 6
Notice that 6 = HCF(90,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 516, 990, 90 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 516, 990, 90?
Answer: HCF of 516, 990, 90 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 990, 90 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 990, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.