Highest Common Factor of 748, 880, 305 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, 880, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 748, 880, 305 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, 880, 305 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, 880, 305 is 1.

HCF(748, 880, 305) = 1

HCF of 748, 880, 305 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, 880, 305 is 1.

Highest Common Factor of 748,880,305 using Euclid's algorithm

Highest Common Factor of 748,880,305 is 1

Step 1: Since 880 > 748, we apply the division lemma to 880 and 748, to get

880 = 748 x 1 + 132

Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 132 and 748, to get

748 = 132 x 5 + 88

Step 3: We consider the new divisor 132 and the new remainder 88, and apply the division lemma to get

132 = 88 x 1 + 44

We consider the new divisor 88 and the new remainder 44, and apply the division lemma to get

88 = 44 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 44, the HCF of 748 and 880 is 44

Notice that 44 = HCF(88,44) = HCF(132,88) = HCF(748,132) = HCF(880,748) .

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

Step 1: Since 305 > 44, we apply the division lemma to 305 and 44, to get

305 = 44 x 6 + 41

Step 2: Since the reminder 44 ≠ 0, we apply division lemma to 41 and 44, to get

44 = 41 x 1 + 3

Step 3: We consider the new divisor 41 and the new remainder 3, and apply the division lemma to get

41 = 3 x 13 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 44 and 305 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(41,3) = HCF(44,41) = HCF(305,44) .

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Frequently Asked Questions on HCF of 748, 880, 305 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, 880, 305?

Answer: HCF of 748, 880, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 748, 880, 305 using Euclid's Algorithm?

Answer: For arbitrary numbers 748, 880, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.