Highest Common Factor of 783, 74 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 783, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 783, 74 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 783, 74 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 783, 74 is 1.

HCF(783, 74) = 1

HCF of 783, 74 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 783, 74 is 1.

Highest Common Factor of 783,74 using Euclid's algorithm

Highest Common Factor of 783,74 is 1

Step 1: Since 783 > 74, we apply the division lemma to 783 and 74, to get

783 = 74 x 10 + 43

Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 43 and 74, to get

74 = 43 x 1 + 31

Step 3: We consider the new divisor 43 and the new remainder 31, and apply the division lemma to get

43 = 31 x 1 + 12

We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get

31 = 12 x 2 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 783 and 74 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(43,31) = HCF(74,43) = HCF(783,74) .

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Frequently Asked Questions on HCF of 783, 74 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 783, 74?

Answer: HCF of 783, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 783, 74 using Euclid's Algorithm?

Answer: For arbitrary numbers 783, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.