Highest Common Factor of 125, 578, 160 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 125, 578, 160 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 125, 578, 160 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 125, 578, 160 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 125, 578, 160 is 1.

HCF(125, 578, 160) = 1

HCF of 125, 578, 160 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 125, 578, 160 is 1.

Highest Common Factor of 125,578,160 using Euclid's algorithm

Highest Common Factor of 125,578,160 is 1

Step 1: Since 578 > 125, we apply the division lemma to 578 and 125, to get

578 = 125 x 4 + 78

Step 2: Since the reminder 125 ≠ 0, we apply division lemma to 78 and 125, to get

125 = 78 x 1 + 47

Step 3: We consider the new divisor 78 and the new remainder 47, and apply the division lemma to get

78 = 47 x 1 + 31

We consider the new divisor 47 and the new remainder 31,and apply the division lemma to get

47 = 31 x 1 + 16

We consider the new divisor 31 and the new remainder 16,and apply the division lemma to get

31 = 16 x 1 + 15

We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get

16 = 15 x 1 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 125 and 578 is 1

Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(31,16) = HCF(47,31) = HCF(78,47) = HCF(125,78) = HCF(578,125) .

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

Step 1: Since 160 > 1, we apply the division lemma to 160 and 1, to get

160 = 1 x 160 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 160 is 1

Notice that 1 = HCF(160,1) .

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Frequently Asked Questions on HCF of 125, 578, 160 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 125, 578, 160?

Answer: HCF of 125, 578, 160 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 125, 578, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 125, 578, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.