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 221, 648 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 221, 648 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 221, 648 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 221, 648 is 1.
HCF(221, 648) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 221, 648 is 1.
Step 1: Since 648 > 221, we apply the division lemma to 648 and 221, to get
648 = 221 x 2 + 206
Step 2: Since the reminder 221 ≠ 0, we apply division lemma to 206 and 221, to get
221 = 206 x 1 + 15
Step 3: We consider the new divisor 206 and the new remainder 15, and apply the division lemma to get
206 = 15 x 13 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 221 and 648 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(206,15) = HCF(221,206) = HCF(648,221) .
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 221, 648?
Answer: HCF of 221, 648 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 221, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 221, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.