Highest Common Factor of 370, 503, 27, 332 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 370, 503, 27, 332 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 370, 503, 27, 332 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 370, 503, 27, 332 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 370, 503, 27, 332 is 1.

HCF(370, 503, 27, 332) = 1

HCF of 370, 503, 27, 332 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 370, 503, 27, 332 is 1.

Highest Common Factor of 370,503,27,332 using Euclid's algorithm

Highest Common Factor of 370,503,27,332 is 1

Step 1: Since 503 > 370, we apply the division lemma to 503 and 370, to get

503 = 370 x 1 + 133

Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 133 and 370, to get

370 = 133 x 2 + 104

Step 3: We consider the new divisor 133 and the new remainder 104, and apply the division lemma to get

133 = 104 x 1 + 29

We consider the new divisor 104 and the new remainder 29,and apply the division lemma to get

104 = 29 x 3 + 17

We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get

29 = 17 x 1 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 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 370 and 503 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(104,29) = HCF(133,104) = HCF(370,133) = HCF(503,370) .

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

Step 1: Since 27 > 1, we apply the division lemma to 27 and 1, to get

27 = 1 x 27 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 27 is 1

Notice that 1 = HCF(27,1) .

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

Step 1: Since 332 > 1, we apply the division lemma to 332 and 1, to get

332 = 1 x 332 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 332 is 1

Notice that 1 = HCF(332,1) .

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Frequently Asked Questions on HCF of 370, 503, 27, 332 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 370, 503, 27, 332?

Answer: HCF of 370, 503, 27, 332 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 370, 503, 27, 332 using Euclid's Algorithm?

Answer: For arbitrary numbers 370, 503, 27, 332 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.