Highest Common Factor of 914, 852, 919 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 914, 852, 919 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 914, 852, 919 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 914, 852, 919 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 914, 852, 919 is 1.

HCF(914, 852, 919) = 1

HCF of 914, 852, 919 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 914, 852, 919 is 1.

Highest Common Factor of 914,852,919 using Euclid's algorithm

Highest Common Factor of 914,852,919 is 1

Step 1: Since 914 > 852, we apply the division lemma to 914 and 852, to get

914 = 852 x 1 + 62

Step 2: Since the reminder 852 ≠ 0, we apply division lemma to 62 and 852, to get

852 = 62 x 13 + 46

Step 3: We consider the new divisor 62 and the new remainder 46, and apply the division lemma to get

62 = 46 x 1 + 16

We consider the new divisor 46 and the new remainder 16,and apply the division lemma to get

46 = 16 x 2 + 14

We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get

16 = 14 x 1 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 914 and 852 is 2

Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(46,16) = HCF(62,46) = HCF(852,62) = HCF(914,852) .

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

Step 1: Since 919 > 2, we apply the division lemma to 919 and 2, to get

919 = 2 x 459 + 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 919 is 1

Notice that 1 = HCF(2,1) = HCF(919,2) .

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Frequently Asked Questions on HCF of 914, 852, 919 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 914, 852, 919?

Answer: HCF of 914, 852, 919 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 914, 852, 919 using Euclid's Algorithm?

Answer: For arbitrary numbers 914, 852, 919 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.