Highest Common Factor of 624, 401, 448 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 624, 401, 448 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 624, 401, 448 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 624, 401, 448 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 624, 401, 448 is 1.

HCF(624, 401, 448) = 1

HCF of 624, 401, 448 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 624, 401, 448 is 1.

Highest Common Factor of 624,401,448 using Euclid's algorithm

Highest Common Factor of 624,401,448 is 1

Step 1: Since 624 > 401, we apply the division lemma to 624 and 401, to get

624 = 401 x 1 + 223

Step 2: Since the reminder 401 ≠ 0, we apply division lemma to 223 and 401, to get

401 = 223 x 1 + 178

Step 3: We consider the new divisor 223 and the new remainder 178, and apply the division lemma to get

223 = 178 x 1 + 45

We consider the new divisor 178 and the new remainder 45,and apply the division lemma to get

178 = 45 x 3 + 43

We consider the new divisor 45 and the new remainder 43,and apply the division lemma to get

45 = 43 x 1 + 2

We consider the new divisor 43 and the new remainder 2,and apply the division lemma to get

43 = 2 x 21 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 624 and 401 is 1

Notice that 1 = HCF(2,1) = HCF(43,2) = HCF(45,43) = HCF(178,45) = HCF(223,178) = HCF(401,223) = HCF(624,401) .

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

Step 1: Since 448 > 1, we apply the division lemma to 448 and 1, to get

448 = 1 x 448 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 448 is 1

Notice that 1 = HCF(448,1) .

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Frequently Asked Questions on HCF of 624, 401, 448 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 624, 401, 448?

Answer: HCF of 624, 401, 448 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 624, 401, 448 using Euclid's Algorithm?

Answer: For arbitrary numbers 624, 401, 448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.