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 650, 820, 572 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 650, 820, 572 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 650, 820, 572 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 650, 820, 572 is 2.
HCF(650, 820, 572) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 650, 820, 572 is 2.
Step 1: Since 820 > 650, we apply the division lemma to 820 and 650, to get
820 = 650 x 1 + 170
Step 2: Since the reminder 650 ≠ 0, we apply division lemma to 170 and 650, to get
650 = 170 x 3 + 140
Step 3: We consider the new divisor 170 and the new remainder 140, and apply the division lemma to get
170 = 140 x 1 + 30
We consider the new divisor 140 and the new remainder 30,and apply the division lemma to get
140 = 30 x 4 + 20
We consider the new divisor 30 and the new remainder 20,and apply the division lemma to get
30 = 20 x 1 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 650 and 820 is 10
Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(140,30) = HCF(170,140) = HCF(650,170) = HCF(820,650) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 572 > 10, we apply the division lemma to 572 and 10, to get
572 = 10 x 57 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 572 is 2
Notice that 2 = HCF(10,2) = HCF(572,10) .
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 650, 820, 572?
Answer: HCF of 650, 820, 572 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 650, 820, 572 using Euclid's Algorithm?
Answer: For arbitrary numbers 650, 820, 572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.