Highest Common Factor of 216, 368 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 216, 368 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 216, 368 is 8 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 216, 368 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 216, 368 is 8.
HCF(216, 368) = 8
HCF of 216, 368 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 216, 368 is 8.
Highest Common Factor of 216,368 is 8
Step 1: Since 368 > 216, we apply the division lemma to 368 and 216, to get
368 = 216 x 1 + 152
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 152 and 216, to get
216 = 152 x 1 + 64
Step 3: We consider the new divisor 152 and the new remainder 64, and apply the division lemma to get
152 = 64 x 2 + 24
We consider the new divisor 64 and the new remainder 24,and apply the division lemma to get
64 = 24 x 2 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 216 and 368 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) = HCF(152,64) = HCF(216,152) = HCF(368,216) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 216, 368 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 216, 368?
Answer: HCF of 216, 368 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 216, 368 using Euclid's Algorithm?
Answer: For arbitrary numbers 216, 368 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.