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 513, 825, 495 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 825, 495 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 513, 825, 495 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 513, 825, 495 is 3.
HCF(513, 825, 495) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 825, 495 is 3.
Step 1: Since 825 > 513, we apply the division lemma to 825 and 513, to get
825 = 513 x 1 + 312
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 312 and 513, to get
513 = 312 x 1 + 201
Step 3: We consider the new divisor 312 and the new remainder 201, and apply the division lemma to get
312 = 201 x 1 + 111
We consider the new divisor 201 and the new remainder 111,and apply the division lemma to get
201 = 111 x 1 + 90
We consider the new divisor 111 and the new remainder 90,and apply the division lemma to get
111 = 90 x 1 + 21
We consider the new divisor 90 and the new remainder 21,and apply the division lemma to get
90 = 21 x 4 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 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 513 and 825 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(90,21) = HCF(111,90) = HCF(201,111) = HCF(312,201) = HCF(513,312) = HCF(825,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 495 > 3, we apply the division lemma to 495 and 3, to get
495 = 3 x 165 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 495 is 3
Notice that 3 = HCF(495,3) .
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 513, 825, 495?
Answer: HCF of 513, 825, 495 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 825, 495 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 825, 495 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.