Highest Common Factor of 145, 676, 746 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 145, 676, 746 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 145, 676, 746 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 145, 676, 746 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 145, 676, 746 is 1.

HCF(145, 676, 746) = 1

HCF of 145, 676, 746 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 145, 676, 746 is 1.

Highest Common Factor of 145,676,746 using Euclid's algorithm

Highest Common Factor of 145,676,746 is 1

Step 1: Since 676 > 145, we apply the division lemma to 676 and 145, to get

676 = 145 x 4 + 96

Step 2: Since the reminder 145 ≠ 0, we apply division lemma to 96 and 145, to get

145 = 96 x 1 + 49

Step 3: We consider the new divisor 96 and the new remainder 49, and apply the division lemma to get

96 = 49 x 1 + 47

We consider the new divisor 49 and the new remainder 47,and apply the division lemma to get

49 = 47 x 1 + 2

We consider the new divisor 47 and the new remainder 2,and apply the division lemma to get

47 = 2 x 23 + 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 145 and 676 is 1

Notice that 1 = HCF(2,1) = HCF(47,2) = HCF(49,47) = HCF(96,49) = HCF(145,96) = HCF(676,145) .

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

Step 1: Since 746 > 1, we apply the division lemma to 746 and 1, to get

746 = 1 x 746 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 746 is 1

Notice that 1 = HCF(746,1) .

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Frequently Asked Questions on HCF of 145, 676, 746 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 145, 676, 746?

Answer: HCF of 145, 676, 746 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 145, 676, 746 using Euclid's Algorithm?

Answer: For arbitrary numbers 145, 676, 746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.