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 224, 649, 353, 81 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 224, 649, 353, 81 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 224, 649, 353, 81 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 224, 649, 353, 81 is 1.
HCF(224, 649, 353, 81) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 224, 649, 353, 81 is 1.
Step 1: Since 649 > 224, we apply the division lemma to 649 and 224, to get
649 = 224 x 2 + 201
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 201 and 224, to get
224 = 201 x 1 + 23
Step 3: We consider the new divisor 201 and the new remainder 23, and apply the division lemma to get
201 = 23 x 8 + 17
We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get
23 = 17 x 1 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 224 and 649 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(201,23) = HCF(224,201) = HCF(649,224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 353 > 1, we apply the division lemma to 353 and 1, to get
353 = 1 x 353 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 353 is 1
Notice that 1 = HCF(353,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 81 > 1, we apply the division lemma to 81 and 1, to get
81 = 1 x 81 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 81 is 1
Notice that 1 = HCF(81,1) .
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 224, 649, 353, 81?
Answer: HCF of 224, 649, 353, 81 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 224, 649, 353, 81 using Euclid's Algorithm?
Answer: For arbitrary numbers 224, 649, 353, 81 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.