Highest Common Factor of 369, 890, 121 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 369, 890, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 369, 890, 121 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 369, 890, 121 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 369, 890, 121 is 1.

HCF(369, 890, 121) = 1

HCF of 369, 890, 121 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 369, 890, 121 is 1.

Highest Common Factor of 369,890,121 using Euclid's algorithm

Highest Common Factor of 369,890,121 is 1

Step 1: Since 890 > 369, we apply the division lemma to 890 and 369, to get

890 = 369 x 2 + 152

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 152 and 369, to get

369 = 152 x 2 + 65

Step 3: We consider the new divisor 152 and the new remainder 65, and apply the division lemma to get

152 = 65 x 2 + 22

We consider the new divisor 65 and the new remainder 22,and apply the division lemma to get

65 = 22 x 2 + 21

We consider the new divisor 22 and the new remainder 21,and apply the division lemma to get

22 = 21 x 1 + 1

We consider the new divisor 21 and the new remainder 1,and apply the division lemma to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 369 and 890 is 1

Notice that 1 = HCF(21,1) = HCF(22,21) = HCF(65,22) = HCF(152,65) = HCF(369,152) = HCF(890,369) .

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

Step 1: Since 121 > 1, we apply the division lemma to 121 and 1, to get

121 = 1 x 121 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 121 is 1

Notice that 1 = HCF(121,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 369, 890, 121 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 369, 890, 121?

Answer: HCF of 369, 890, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 369, 890, 121 using Euclid's Algorithm?

Answer: For arbitrary numbers 369, 890, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.