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 520, 540, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 520, 540, 829 is 1 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 520, 540, 829 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 520, 540, 829 is 1.
HCF(520, 540, 829) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 520, 540, 829 is 1.
Step 1: Since 540 > 520, we apply the division lemma to 540 and 520, to get
540 = 520 x 1 + 20
Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 20 and 520, to get
520 = 20 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 520 and 540 is 20
Notice that 20 = HCF(520,20) = HCF(540,520) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 829 > 20, we apply the division lemma to 829 and 20, to get
829 = 20 x 41 + 9
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 9 and 20, to get
20 = 9 x 2 + 2
Step 3: We consider the new divisor 9 and the new remainder 2, and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 829 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(829,20) .
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 520, 540, 829?
Answer: HCF of 520, 540, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 520, 540, 829 using Euclid's Algorithm?
Answer: For arbitrary numbers 520, 540, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.