Highest Common Factor of 142, 528, 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 142, 528, 245 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 142, 528, 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 142, 528, 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 142, 528, 245 is 1.

HCF(142, 528, 245) = 1

HCF of 142, 528, 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 142, 528, 245 is 1.

Highest Common Factor of 142,528,245 using Euclid's algorithm

Highest Common Factor of 142,528,245 is 1

Step 1: Since 528 > 142, we apply the division lemma to 528 and 142, to get

528 = 142 x 3 + 102

Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 102 and 142, to get

142 = 102 x 1 + 40

Step 3: We consider the new divisor 102 and the new remainder 40, and apply the division lemma to get

102 = 40 x 2 + 22

We consider the new divisor 40 and the new remainder 22,and apply the division lemma to get

40 = 22 x 1 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 142 and 528 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(40,22) = HCF(102,40) = HCF(142,102) = HCF(528,142) .

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

Step 1: Since 245 > 2, we apply the division lemma to 245 and 2, to get

245 = 2 x 122 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 245 is 1

Notice that 1 = HCF(2,1) = HCF(245,2) .

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Frequently Asked Questions on HCF of 142, 528, 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 142, 528, 245?

Answer: HCF of 142, 528, 245 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 142, 528, 245 using Euclid's Algorithm?

Answer: For arbitrary numbers 142, 528, 245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.