Highest Common Factor of 141, 748, 245 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 141, 748, 245 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 141, 748, 245 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 141, 748, 245 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 141, 748, 245 is 1.

HCF(141, 748, 245) = 1

HCF of 141, 748, 245 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 141, 748, 245 is 1.

Highest Common Factor of 141,748,245 using Euclid's algorithm

Highest Common Factor of 141,748,245 is 1

Step 1: Since 748 > 141, we apply the division lemma to 748 and 141, to get

748 = 141 x 5 + 43

Step 2: Since the reminder 141 ≠ 0, we apply division lemma to 43 and 141, to get

141 = 43 x 3 + 12

Step 3: We consider the new divisor 43 and the new remainder 12, and apply the division lemma to get

43 = 12 x 3 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 141 and 748 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(141,43) = HCF(748,141) .

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

Step 1: Since 245 > 1, we apply the division lemma to 245 and 1, to get

245 = 1 x 245 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 245 is 1

Notice that 1 = HCF(245,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 141, 748, 245 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 141, 748, 245?

Answer: HCF of 141, 748, 245 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 141, 748, 245 using Euclid's Algorithm?

Answer: For arbitrary numbers 141, 748, 245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.