Highest Common Factor of 142, 965, 69 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, 965, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 142, 965, 69 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, 965, 69 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, 965, 69 is 1.

HCF(142, 965, 69) = 1

HCF of 142, 965, 69 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, 965, 69 is 1.

Highest Common Factor of 142,965,69 using Euclid's algorithm

Highest Common Factor of 142,965,69 is 1

Step 1: Since 965 > 142, we apply the division lemma to 965 and 142, to get

965 = 142 x 6 + 113

Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 113 and 142, to get

142 = 113 x 1 + 29

Step 3: We consider the new divisor 113 and the new remainder 29, and apply the division lemma to get

113 = 29 x 3 + 26

We consider the new divisor 29 and the new remainder 26,and apply the division lemma to get

29 = 26 x 1 + 3

We consider the new divisor 26 and the new remainder 3,and apply the division lemma to get

26 = 3 x 8 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 142 and 965 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(29,26) = HCF(113,29) = HCF(142,113) = HCF(965,142) .

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

Step 1: Since 69 > 1, we apply the division lemma to 69 and 1, to get

69 = 1 x 69 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 69 is 1

Notice that 1 = HCF(69,1) .

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Frequently Asked Questions on HCF of 142, 965, 69 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, 965, 69?

Answer: HCF of 142, 965, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 142, 965, 69 using Euclid's Algorithm?

Answer: For arbitrary numbers 142, 965, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.