Highest Common Factor of 998, 727, 921, 62 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 998, 727, 921, 62 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 998, 727, 921, 62 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 998, 727, 921, 62 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 998, 727, 921, 62 is 1.

HCF(998, 727, 921, 62) = 1

HCF of 998, 727, 921, 62 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 998, 727, 921, 62 is 1.

Highest Common Factor of 998,727,921,62 using Euclid's algorithm

Highest Common Factor of 998,727,921,62 is 1

Step 1: Since 998 > 727, we apply the division lemma to 998 and 727, to get

998 = 727 x 1 + 271

Step 2: Since the reminder 727 ≠ 0, we apply division lemma to 271 and 727, to get

727 = 271 x 2 + 185

Step 3: We consider the new divisor 271 and the new remainder 185, and apply the division lemma to get

271 = 185 x 1 + 86

We consider the new divisor 185 and the new remainder 86,and apply the division lemma to get

185 = 86 x 2 + 13

We consider the new divisor 86 and the new remainder 13,and apply the division lemma to get

86 = 13 x 6 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 998 and 727 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(86,13) = HCF(185,86) = HCF(271,185) = HCF(727,271) = HCF(998,727) .

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

Step 1: Since 921 > 1, we apply the division lemma to 921 and 1, to get

921 = 1 x 921 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 921 is 1

Notice that 1 = HCF(921,1) .

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

Step 1: Since 62 > 1, we apply the division lemma to 62 and 1, to get

62 = 1 x 62 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 62 is 1

Notice that 1 = HCF(62,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 998, 727, 921, 62 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 998, 727, 921, 62?

Answer: HCF of 998, 727, 921, 62 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 998, 727, 921, 62 using Euclid's Algorithm?

Answer: For arbitrary numbers 998, 727, 921, 62 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.