Highest Common Factor of 224, 704, 405 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 224, 704, 405 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 224, 704, 405 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, 704, 405 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, 704, 405 is 1.
HCF(224, 704, 405) = 1
HCF of 224, 704, 405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 224, 704, 405 is 1.
Highest Common Factor of 224,704,405 is 1
Step 1: Since 704 > 224, we apply the division lemma to 704 and 224, to get
704 = 224 x 3 + 32
Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 32 and 224, to get
224 = 32 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 224 and 704 is 32
Notice that 32 = HCF(224,32) = HCF(704,224) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 405 > 32, we apply the division lemma to 405 and 32, to get
405 = 32 x 12 + 21
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 21 and 32, to get
32 = 21 x 1 + 11
Step 3: We consider the new divisor 21 and the new remainder 11, and apply the division lemma to get
21 = 11 x 1 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 405 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(405,32) .
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Frequently Asked Questions on HCF of 224, 704, 405 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 224, 704, 405?
Answer: HCF of 224, 704, 405 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 224, 704, 405 using Euclid's Algorithm?
Answer: For arbitrary numbers 224, 704, 405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
