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 572, 8316, 2795 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 572, 8316, 2795 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 572, 8316, 2795 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 572, 8316, 2795 is 1.
HCF(572, 8316, 2795) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 572, 8316, 2795 is 1.
Step 1: Since 8316 > 572, we apply the division lemma to 8316 and 572, to get
8316 = 572 x 14 + 308
Step 2: Since the reminder 572 ≠ 0, we apply division lemma to 308 and 572, to get
572 = 308 x 1 + 264
Step 3: We consider the new divisor 308 and the new remainder 264, and apply the division lemma to get
308 = 264 x 1 + 44
We consider the new divisor 264 and the new remainder 44, and apply the division lemma to get
264 = 44 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 44, the HCF of 572 and 8316 is 44
Notice that 44 = HCF(264,44) = HCF(308,264) = HCF(572,308) = HCF(8316,572) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2795 > 44, we apply the division lemma to 2795 and 44, to get
2795 = 44 x 63 + 23
Step 2: Since the reminder 44 ≠ 0, we apply division lemma to 23 and 44, to get
44 = 23 x 1 + 21
Step 3: We consider the new divisor 23 and the new remainder 21, and apply the division lemma to get
23 = 21 x 1 + 2
We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get
21 = 2 x 10 + 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 44 and 2795 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(44,23) = HCF(2795,44) .
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 572, 8316, 2795?
Answer: HCF of 572, 8316, 2795 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 572, 8316, 2795 using Euclid's Algorithm?
Answer: For arbitrary numbers 572, 8316, 2795 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.