HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 65, 143, 169 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 65, 143, 169 is 13 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 65, 143, 169 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 65, 143, 169 is **13**.

HCF(65, 143, 169) = 13

*Highest common factor* or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

Highest common factor (HCF) of 65, 143, 169 is **13**.

**Step 1:** Since 143 > 65, we apply the division lemma to 143 and 65, to get

143 = 65 x 2 + 13

**Step 2:** Since the reminder 65 ≠ 0, we apply division lemma to 13 and 65, to get

65 = 13 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 65 and 143 is 13

Notice that 13 = HCF(65,13) = HCF(143,65) .

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

**Step 1:** Since 169 > 13, we apply the division lemma to 169 and 13, to get

169 = 13 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 169 is 13

Notice that 13 = HCF(169,13) .

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

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 65, 143, 169?

Answer: HCF of 65, 143, 169 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 65, 143, 169 using Euclid's Algorithm?

Answer: For arbitrary numbers 65, 143, 169 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.