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 564, 903, 921 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 903, 921 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 564, 903, 921 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 564, 903, 921 is 3.
HCF(564, 903, 921) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 564, 903, 921 is 3.
Step 1: Since 903 > 564, we apply the division lemma to 903 and 564, to get
903 = 564 x 1 + 339
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 339 and 564, to get
564 = 339 x 1 + 225
Step 3: We consider the new divisor 339 and the new remainder 225, and apply the division lemma to get
339 = 225 x 1 + 114
We consider the new divisor 225 and the new remainder 114,and apply the division lemma to get
225 = 114 x 1 + 111
We consider the new divisor 114 and the new remainder 111,and apply the division lemma to get
114 = 111 x 1 + 3
We consider the new divisor 111 and the new remainder 3,and apply the division lemma to get
111 = 3 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 564 and 903 is 3
Notice that 3 = HCF(111,3) = HCF(114,111) = HCF(225,114) = HCF(339,225) = HCF(564,339) = HCF(903,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 921 > 3, we apply the division lemma to 921 and 3, to get
921 = 3 x 307 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 921 is 3
Notice that 3 = HCF(921,3) .
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 564, 903, 921?
Answer: HCF of 564, 903, 921 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 903, 921 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 903, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.