Highest Common Factor of 8496, 7312 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 8496, 7312 i.e. 16 the largest integer that leaves a remainder zero for all numbers.

HCF of 8496, 7312 is 16 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 8496, 7312 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 8496, 7312 is 16.

HCF(8496, 7312) = 16

HCF of 8496, 7312 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 8496, 7312 is 16.

Highest Common Factor of 8496,7312 using Euclid's algorithm

Highest Common Factor of 8496,7312 is 16

Step 1: Since 8496 > 7312, we apply the division lemma to 8496 and 7312, to get

8496 = 7312 x 1 + 1184

Step 2: Since the reminder 7312 ≠ 0, we apply division lemma to 1184 and 7312, to get

7312 = 1184 x 6 + 208

Step 3: We consider the new divisor 1184 and the new remainder 208, and apply the division lemma to get

1184 = 208 x 5 + 144

We consider the new divisor 208 and the new remainder 144,and apply the division lemma to get

208 = 144 x 1 + 64

We consider the new divisor 144 and the new remainder 64,and apply the division lemma to get

144 = 64 x 2 + 16

We consider the new divisor 64 and the new remainder 16,and apply the division lemma to get

64 = 16 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 8496 and 7312 is 16

Notice that 16 = HCF(64,16) = HCF(144,64) = HCF(208,144) = HCF(1184,208) = HCF(7312,1184) = HCF(8496,7312) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 8496, 7312 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 8496, 7312?

Answer: HCF of 8496, 7312 is 16 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8496, 7312 using Euclid's Algorithm?

Answer: For arbitrary numbers 8496, 7312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.