Highest Common Factor of 748, 434, 125 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 748, 434, 125 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 748, 434, 125 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 748, 434, 125 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 748, 434, 125 is 1.

HCF(748, 434, 125) = 1

HCF of 748, 434, 125 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 748, 434, 125 is 1.

Highest Common Factor of 748,434,125 using Euclid's algorithm

Highest Common Factor of 748,434,125 is 1

Step 1: Since 748 > 434, we apply the division lemma to 748 and 434, to get

748 = 434 x 1 + 314

Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 314 and 434, to get

434 = 314 x 1 + 120

Step 3: We consider the new divisor 314 and the new remainder 120, and apply the division lemma to get

314 = 120 x 2 + 74

We consider the new divisor 120 and the new remainder 74,and apply the division lemma to get

120 = 74 x 1 + 46

We consider the new divisor 74 and the new remainder 46,and apply the division lemma to get

74 = 46 x 1 + 28

We consider the new divisor 46 and the new remainder 28,and apply the division lemma to get

46 = 28 x 1 + 18

We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get

28 = 18 x 1 + 10

We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get

18 = 10 x 1 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 748 and 434 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(46,28) = HCF(74,46) = HCF(120,74) = HCF(314,120) = HCF(434,314) = HCF(748,434) .

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

Step 1: Since 125 > 2, we apply the division lemma to 125 and 2, to get

125 = 2 x 62 + 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 125 is 1

Notice that 1 = HCF(2,1) = HCF(125,2) .

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Frequently Asked Questions on HCF of 748, 434, 125 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 748, 434, 125?

Answer: HCF of 748, 434, 125 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 748, 434, 125 using Euclid's Algorithm?

Answer: For arbitrary numbers 748, 434, 125 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.