Highest Common Factor of 370, 237, 669 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, 237, 669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 370, 237, 669 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, 237, 669 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, 237, 669 is 1.

HCF(370, 237, 669) = 1

HCF of 370, 237, 669 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, 237, 669 is 1.

Highest Common Factor of 370,237,669 using Euclid's algorithm

Highest Common Factor of 370,237,669 is 1

Step 1: Since 370 > 237, we apply the division lemma to 370 and 237, to get

370 = 237 x 1 + 133

Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 133 and 237, to get

237 = 133 x 1 + 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 237 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(237,133) = HCF(370,237) .

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

Step 1: Since 669 > 1, we apply the division lemma to 669 and 1, to get

669 = 1 x 669 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1

Notice that 1 = HCF(669,1) .

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Frequently Asked Questions on HCF of 370, 237, 669 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, 237, 669?

Answer: HCF of 370, 237, 669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 370, 237, 669 using Euclid's Algorithm?

Answer: For arbitrary numbers 370, 237, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.