Highest Common Factor of 986, 699, 825 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 986, 699, 825 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 986, 699, 825 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 986, 699, 825 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 986, 699, 825 is 1.

HCF(986, 699, 825) = 1

HCF of 986, 699, 825 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 986, 699, 825 is 1.

Highest Common Factor of 986,699,825 using Euclid's algorithm

Highest Common Factor of 986,699,825 is 1

Step 1: Since 986 > 699, we apply the division lemma to 986 and 699, to get

986 = 699 x 1 + 287

Step 2: Since the reminder 699 ≠ 0, we apply division lemma to 287 and 699, to get

699 = 287 x 2 + 125

Step 3: We consider the new divisor 287 and the new remainder 125, and apply the division lemma to get

287 = 125 x 2 + 37

We consider the new divisor 125 and the new remainder 37,and apply the division lemma to get

125 = 37 x 3 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 986 and 699 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(125,37) = HCF(287,125) = HCF(699,287) = HCF(986,699) .

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

Step 1: Since 825 > 1, we apply the division lemma to 825 and 1, to get

825 = 1 x 825 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 825 is 1

Notice that 1 = HCF(825,1) .

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Frequently Asked Questions on HCF of 986, 699, 825 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 986, 699, 825?

Answer: HCF of 986, 699, 825 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 986, 699, 825 using Euclid's Algorithm?

Answer: For arbitrary numbers 986, 699, 825 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.