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 573, 8909, 8523 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 573, 8909, 8523 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 573, 8909, 8523 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 573, 8909, 8523 is 1.
HCF(573, 8909, 8523) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 573, 8909, 8523 is 1.
Step 1: Since 8909 > 573, we apply the division lemma to 8909 and 573, to get
8909 = 573 x 15 + 314
Step 2: Since the reminder 573 ≠ 0, we apply division lemma to 314 and 573, to get
573 = 314 x 1 + 259
Step 3: We consider the new divisor 314 and the new remainder 259, and apply the division lemma to get
314 = 259 x 1 + 55
We consider the new divisor 259 and the new remainder 55,and apply the division lemma to get
259 = 55 x 4 + 39
We consider the new divisor 55 and the new remainder 39,and apply the division lemma to get
55 = 39 x 1 + 16
We consider the new divisor 39 and the new remainder 16,and apply the division lemma to get
39 = 16 x 2 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 573 and 8909 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(39,16) = HCF(55,39) = HCF(259,55) = HCF(314,259) = HCF(573,314) = HCF(8909,573) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8523 > 1, we apply the division lemma to 8523 and 1, to get
8523 = 1 x 8523 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8523 is 1
Notice that 1 = HCF(8523,1) .
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 573, 8909, 8523?
Answer: HCF of 573, 8909, 8523 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 573, 8909, 8523 using Euclid's Algorithm?
Answer: For arbitrary numbers 573, 8909, 8523 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.