Highest Common Factor of 448, 2561, 8212 using Euclid's algorithm
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 448, 2561, 8212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 2561, 8212 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 448, 2561, 8212 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 448, 2561, 8212 is 1.
HCF(448, 2561, 8212) = 1
HCF of 448, 2561, 8212 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 2561, 8212 is 1.
Highest Common Factor of 448,2561,8212 is 1
Step 1: Since 2561 > 448, we apply the division lemma to 2561 and 448, to get
2561 = 448 x 5 + 321
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 321 and 448, to get
448 = 321 x 1 + 127
Step 3: We consider the new divisor 321 and the new remainder 127, and apply the division lemma to get
321 = 127 x 2 + 67
We consider the new divisor 127 and the new remainder 67,and apply the division lemma to get
127 = 67 x 1 + 60
We consider the new divisor 67 and the new remainder 60,and apply the division lemma to get
67 = 60 x 1 + 7
We consider the new divisor 60 and the new remainder 7,and apply the division lemma to get
60 = 7 x 8 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 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 448 and 2561 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(60,7) = HCF(67,60) = HCF(127,67) = HCF(321,127) = HCF(448,321) = HCF(2561,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8212 > 1, we apply the division lemma to 8212 and 1, to get
8212 = 1 x 8212 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8212 is 1
Notice that 1 = HCF(8212,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 448, 2561, 8212 using Euclid's Algorithm
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 448, 2561, 8212?
Answer: HCF of 448, 2561, 8212 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 2561, 8212 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 2561, 8212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.