Highest Common Factor of 975, 388, 22 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 975, 388, 22 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 975, 388, 22 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 975, 388, 22 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 975, 388, 22 is 1.

HCF(975, 388, 22) = 1

HCF of 975, 388, 22 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 975, 388, 22 is 1.

Highest Common Factor of 975,388,22 using Euclid's algorithm

Highest Common Factor of 975,388,22 is 1

Step 1: Since 975 > 388, we apply the division lemma to 975 and 388, to get

975 = 388 x 2 + 199

Step 2: Since the reminder 388 ≠ 0, we apply division lemma to 199 and 388, to get

388 = 199 x 1 + 189

Step 3: We consider the new divisor 199 and the new remainder 189, and apply the division lemma to get

199 = 189 x 1 + 10

We consider the new divisor 189 and the new remainder 10,and apply the division lemma to get

189 = 10 x 18 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 975 and 388 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(189,10) = HCF(199,189) = HCF(388,199) = HCF(975,388) .

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

Step 1: Since 22 > 1, we apply the division lemma to 22 and 1, to get

22 = 1 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 22 is 1

Notice that 1 = HCF(22,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 975, 388, 22 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 975, 388, 22?

Answer: HCF of 975, 388, 22 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 975, 388, 22 using Euclid's Algorithm?

Answer: For arbitrary numbers 975, 388, 22 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.