Highest Common Factor of 577, 402, 73, 132 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 577, 402, 73, 132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 577, 402, 73, 132 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 577, 402, 73, 132 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 577, 402, 73, 132 is 1.

HCF(577, 402, 73, 132) = 1

HCF of 577, 402, 73, 132 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 577, 402, 73, 132 is 1.

Highest Common Factor of 577,402,73,132 using Euclid's algorithm

Highest Common Factor of 577,402,73,132 is 1

Step 1: Since 577 > 402, we apply the division lemma to 577 and 402, to get

577 = 402 x 1 + 175

Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 175 and 402, to get

402 = 175 x 2 + 52

Step 3: We consider the new divisor 175 and the new remainder 52, and apply the division lemma to get

175 = 52 x 3 + 19

We consider the new divisor 52 and the new remainder 19,and apply the division lemma to get

52 = 19 x 2 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 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 577 and 402 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(52,19) = HCF(175,52) = HCF(402,175) = HCF(577,402) .

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

Step 1: Since 73 > 1, we apply the division lemma to 73 and 1, to get

73 = 1 x 73 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 73 is 1

Notice that 1 = HCF(73,1) .

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

Step 1: Since 132 > 1, we apply the division lemma to 132 and 1, to get

132 = 1 x 132 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 132 is 1

Notice that 1 = HCF(132,1) .

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Frequently Asked Questions on HCF of 577, 402, 73, 132 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 577, 402, 73, 132?

Answer: HCF of 577, 402, 73, 132 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 577, 402, 73, 132 using Euclid's Algorithm?

Answer: For arbitrary numbers 577, 402, 73, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.