Highest Common Factor of 169, 644, 388 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 169, 644, 388 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 169, 644, 388 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 169, 644, 388 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 169, 644, 388 is 1.

HCF(169, 644, 388) = 1

HCF of 169, 644, 388 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 169, 644, 388 is 1.

Highest Common Factor of 169,644,388 using Euclid's algorithm

Highest Common Factor of 169,644,388 is 1

Step 1: Since 644 > 169, we apply the division lemma to 644 and 169, to get

644 = 169 x 3 + 137

Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 137 and 169, to get

169 = 137 x 1 + 32

Step 3: We consider the new divisor 137 and the new remainder 32, and apply the division lemma to get

137 = 32 x 4 + 9

We consider the new divisor 32 and the new remainder 9,and apply the division lemma to get

32 = 9 x 3 + 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 169 and 644 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(137,32) = HCF(169,137) = HCF(644,169) .

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

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

388 = 1 x 388 + 0

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

Notice that 1 = HCF(388,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 169, 644, 388 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 169, 644, 388?

Answer: HCF of 169, 644, 388 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 169, 644, 388 using Euclid's Algorithm?

Answer: For arbitrary numbers 169, 644, 388 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.