Highest Common Factor of 1050, 5874 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 1050, 5874 i.e. 6 the largest integer that leaves a remainder zero for all numbers.

HCF of 1050, 5874 is 6 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 1050, 5874 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 1050, 5874 is 6.

HCF(1050, 5874) = 6

HCF of 1050, 5874 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 1050, 5874 is 6.

Highest Common Factor of 1050,5874 using Euclid's algorithm

Highest Common Factor of 1050,5874 is 6

Step 1: Since 5874 > 1050, we apply the division lemma to 5874 and 1050, to get

5874 = 1050 x 5 + 624

Step 2: Since the reminder 1050 ≠ 0, we apply division lemma to 624 and 1050, to get

1050 = 624 x 1 + 426

Step 3: We consider the new divisor 624 and the new remainder 426, and apply the division lemma to get

624 = 426 x 1 + 198

We consider the new divisor 426 and the new remainder 198,and apply the division lemma to get

426 = 198 x 2 + 30

We consider the new divisor 198 and the new remainder 30,and apply the division lemma to get

198 = 30 x 6 + 18

We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get

30 = 18 x 1 + 12

We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get

18 = 12 x 1 + 6

We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1050 and 5874 is 6

Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(198,30) = HCF(426,198) = HCF(624,426) = HCF(1050,624) = HCF(5874,1050) .

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Frequently Asked Questions on HCF of 1050, 5874 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 1050, 5874?

Answer: HCF of 1050, 5874 is 6 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1050, 5874 using Euclid's Algorithm?

Answer: For arbitrary numbers 1050, 5874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.