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 921, 584, 245 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 921, 584, 245 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 921, 584, 245 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 921, 584, 245 is 1.
HCF(921, 584, 245) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 921, 584, 245 is 1.
Step 1: Since 921 > 584, we apply the division lemma to 921 and 584, to get
921 = 584 x 1 + 337
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 337 and 584, to get
584 = 337 x 1 + 247
Step 3: We consider the new divisor 337 and the new remainder 247, and apply the division lemma to get
337 = 247 x 1 + 90
We consider the new divisor 247 and the new remainder 90,and apply the division lemma to get
247 = 90 x 2 + 67
We consider the new divisor 90 and the new remainder 67,and apply the division lemma to get
90 = 67 x 1 + 23
We consider the new divisor 67 and the new remainder 23,and apply the division lemma to get
67 = 23 x 2 + 21
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 921 and 584 is 1
Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(23,21) = HCF(67,23) = HCF(90,67) = HCF(247,90) = HCF(337,247) = HCF(584,337) = HCF(921,584) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 245 > 1, we apply the division lemma to 245 and 1, to get
245 = 1 x 245 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 245 is 1
Notice that 1 = HCF(245,1) .
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 921, 584, 245?
Answer: HCF of 921, 584, 245 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 921, 584, 245 using Euclid's Algorithm?
Answer: For arbitrary numbers 921, 584, 245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.