Highest Common Factor of 438, 505, 57 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 438, 505, 57 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 438, 505, 57 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 438, 505, 57 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 438, 505, 57 is 1.

HCF(438, 505, 57) = 1

HCF of 438, 505, 57 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 438, 505, 57 is 1.

Highest Common Factor of 438,505,57 using Euclid's algorithm

Highest Common Factor of 438,505,57 is 1

Step 1: Since 505 > 438, we apply the division lemma to 505 and 438, to get

505 = 438 x 1 + 67

Step 2: Since the reminder 438 ≠ 0, we apply division lemma to 67 and 438, to get

438 = 67 x 6 + 36

Step 3: We consider the new divisor 67 and the new remainder 36, and apply the division lemma to get

67 = 36 x 1 + 31

We consider the new divisor 36 and the new remainder 31,and apply the division lemma to get

36 = 31 x 1 + 5

We consider the new divisor 31 and the new remainder 5,and apply the division lemma to get

31 = 5 x 6 + 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 438 and 505 is 1

Notice that 1 = HCF(5,1) = HCF(31,5) = HCF(36,31) = HCF(67,36) = HCF(438,67) = HCF(505,438) .

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

Step 1: Since 57 > 1, we apply the division lemma to 57 and 1, to get

57 = 1 x 57 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 57 is 1

Notice that 1 = HCF(57,1) .

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Frequently Asked Questions on HCF of 438, 505, 57 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 438, 505, 57?

Answer: HCF of 438, 505, 57 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 438, 505, 57 using Euclid's Algorithm?

Answer: For arbitrary numbers 438, 505, 57 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.