Highest Common Factor of 754, 977, 324 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 754, 977, 324 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 754, 977, 324 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 754, 977, 324 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 754, 977, 324 is 1.

HCF(754, 977, 324) = 1

HCF of 754, 977, 324 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 754, 977, 324 is 1.

Highest Common Factor of 754,977,324 using Euclid's algorithm

Highest Common Factor of 754,977,324 is 1

Step 1: Since 977 > 754, we apply the division lemma to 977 and 754, to get

977 = 754 x 1 + 223

Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 223 and 754, to get

754 = 223 x 3 + 85

Step 3: We consider the new divisor 223 and the new remainder 85, and apply the division lemma to get

223 = 85 x 2 + 53

We consider the new divisor 85 and the new remainder 53,and apply the division lemma to get

85 = 53 x 1 + 32

We consider the new divisor 53 and the new remainder 32,and apply the division lemma to get

53 = 32 x 1 + 21

We consider the new divisor 32 and the new remainder 21,and apply the division lemma to get

32 = 21 x 1 + 11

We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get

21 = 11 x 1 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 754 and 977 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(53,32) = HCF(85,53) = HCF(223,85) = HCF(754,223) = HCF(977,754) .

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

Step 1: Since 324 > 1, we apply the division lemma to 324 and 1, to get

324 = 1 x 324 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 324 is 1

Notice that 1 = HCF(324,1) .

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Frequently Asked Questions on HCF of 754, 977, 324 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 754, 977, 324?

Answer: HCF of 754, 977, 324 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 754, 977, 324 using Euclid's Algorithm?

Answer: For arbitrary numbers 754, 977, 324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.