Highest Common Factor of 409, 224, 488 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 409, 224, 488 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 409, 224, 488 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 409, 224, 488 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 409, 224, 488 is 1.

HCF(409, 224, 488) = 1

HCF of 409, 224, 488 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 409, 224, 488 is 1.

Highest Common Factor of 409,224,488 using Euclid's algorithm

Highest Common Factor of 409,224,488 is 1

Step 1: Since 409 > 224, we apply the division lemma to 409 and 224, to get

409 = 224 x 1 + 185

Step 2: Since the reminder 224 ≠ 0, we apply division lemma to 185 and 224, to get

224 = 185 x 1 + 39

Step 3: We consider the new divisor 185 and the new remainder 39, and apply the division lemma to get

185 = 39 x 4 + 29

We consider the new divisor 39 and the new remainder 29,and apply the division lemma to get

39 = 29 x 1 + 10

We consider the new divisor 29 and the new remainder 10,and apply the division lemma to get

29 = 10 x 2 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 224 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(29,10) = HCF(39,29) = HCF(185,39) = HCF(224,185) = HCF(409,224) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 488 > 1, we apply the division lemma to 488 and 1, to get

488 = 1 x 488 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 488 is 1

Notice that 1 = HCF(488,1) .

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Frequently Asked Questions on HCF of 409, 224, 488 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 409, 224, 488?

Answer: HCF of 409, 224, 488 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 409, 224, 488 using Euclid's Algorithm?

Answer: For arbitrary numbers 409, 224, 488 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.