Highest Common Factor of 474, 728, 137 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 474, 728, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 474, 728, 137 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 474, 728, 137 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 474, 728, 137 is 1.

HCF(474, 728, 137) = 1

HCF of 474, 728, 137 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 474, 728, 137 is 1.

Highest Common Factor of 474,728,137 using Euclid's algorithm

Highest Common Factor of 474,728,137 is 1

Step 1: Since 728 > 474, we apply the division lemma to 728 and 474, to get

728 = 474 x 1 + 254

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 254 and 474, to get

474 = 254 x 1 + 220

Step 3: We consider the new divisor 254 and the new remainder 220, and apply the division lemma to get

254 = 220 x 1 + 34

We consider the new divisor 220 and the new remainder 34,and apply the division lemma to get

220 = 34 x 6 + 16

We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get

34 = 16 x 2 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 474 and 728 is 2

Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(220,34) = HCF(254,220) = HCF(474,254) = HCF(728,474) .

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

Step 1: Since 137 > 2, we apply the division lemma to 137 and 2, to get

137 = 2 x 68 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 137 is 1

Notice that 1 = HCF(2,1) = HCF(137,2) .

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Frequently Asked Questions on HCF of 474, 728, 137 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 474, 728, 137?

Answer: HCF of 474, 728, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 474, 728, 137 using Euclid's Algorithm?

Answer: For arbitrary numbers 474, 728, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.