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 8160, 7184 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 8160, 7184 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 8160, 7184 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 8160, 7184 is 16.
HCF(8160, 7184) = 16
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8160, 7184 is 16.
Step 1: Since 8160 > 7184, we apply the division lemma to 8160 and 7184, to get
8160 = 7184 x 1 + 976
Step 2: Since the reminder 7184 ≠ 0, we apply division lemma to 976 and 7184, to get
7184 = 976 x 7 + 352
Step 3: We consider the new divisor 976 and the new remainder 352, and apply the division lemma to get
976 = 352 x 2 + 272
We consider the new divisor 352 and the new remainder 272,and apply the division lemma to get
352 = 272 x 1 + 80
We consider the new divisor 272 and the new remainder 80,and apply the division lemma to get
272 = 80 x 3 + 32
We consider the new divisor 80 and the new remainder 32,and apply the division lemma to get
80 = 32 x 2 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 8160 and 7184 is 16
Notice that 16 = HCF(32,16) = HCF(80,32) = HCF(272,80) = HCF(352,272) = HCF(976,352) = HCF(7184,976) = HCF(8160,7184) .
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 8160, 7184?
Answer: HCF of 8160, 7184 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8160, 7184 using Euclid's Algorithm?
Answer: For arbitrary numbers 8160, 7184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.