Highest Common Factor of 752, 878, 737 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 752, 878, 737 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 752, 878, 737 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 752, 878, 737 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 752, 878, 737 is 1.

HCF(752, 878, 737) = 1

HCF of 752, 878, 737 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 752, 878, 737 is 1.

Highest Common Factor of 752,878,737 using Euclid's algorithm

Highest Common Factor of 752,878,737 is 1

Step 1: Since 878 > 752, we apply the division lemma to 878 and 752, to get

878 = 752 x 1 + 126

Step 2: Since the reminder 752 ≠ 0, we apply division lemma to 126 and 752, to get

752 = 126 x 5 + 122

Step 3: We consider the new divisor 126 and the new remainder 122, and apply the division lemma to get

126 = 122 x 1 + 4

We consider the new divisor 122 and the new remainder 4,and apply the division lemma to get

122 = 4 x 30 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 752 and 878 is 2

Notice that 2 = HCF(4,2) = HCF(122,4) = HCF(126,122) = HCF(752,126) = HCF(878,752) .

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

Step 1: Since 737 > 2, we apply the division lemma to 737 and 2, to get

737 = 2 x 368 + 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 737 is 1

Notice that 1 = HCF(2,1) = HCF(737,2) .

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Frequently Asked Questions on HCF of 752, 878, 737 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 752, 878, 737?

Answer: HCF of 752, 878, 737 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 752, 878, 737 using Euclid's Algorithm?

Answer: For arbitrary numbers 752, 878, 737 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.