Highest Common Factor of 753, 977, 664 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 753, 977, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 753, 977, 664 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 753, 977, 664 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 753, 977, 664 is 1.

HCF(753, 977, 664) = 1

HCF of 753, 977, 664 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 753, 977, 664 is 1.

Highest Common Factor of 753,977,664 using Euclid's algorithm

Highest Common Factor of 753,977,664 is 1

Step 1: Since 977 > 753, we apply the division lemma to 977 and 753, to get

977 = 753 x 1 + 224

Step 2: Since the reminder 753 ≠ 0, we apply division lemma to 224 and 753, to get

753 = 224 x 3 + 81

Step 3: We consider the new divisor 224 and the new remainder 81, and apply the division lemma to get

224 = 81 x 2 + 62

We consider the new divisor 81 and the new remainder 62,and apply the division lemma to get

81 = 62 x 1 + 19

We consider the new divisor 62 and the new remainder 19,and apply the division lemma to get

62 = 19 x 3 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 753 and 977 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(62,19) = HCF(81,62) = HCF(224,81) = HCF(753,224) = HCF(977,753) .

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

Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get

664 = 1 x 664 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1

Notice that 1 = HCF(664,1) .

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Frequently Asked Questions on HCF of 753, 977, 664 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 753, 977, 664?

Answer: HCF of 753, 977, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 753, 977, 664 using Euclid's Algorithm?

Answer: For arbitrary numbers 753, 977, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.