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 299, 510 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 299, 510 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 299, 510 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 299, 510 is 1.
HCF(299, 510) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 299, 510 is 1.
Step 1: Since 510 > 299, we apply the division lemma to 510 and 299, to get
510 = 299 x 1 + 211
Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 211 and 299, to get
299 = 211 x 1 + 88
Step 3: We consider the new divisor 211 and the new remainder 88, and apply the division lemma to get
211 = 88 x 2 + 35
We consider the new divisor 88 and the new remainder 35,and apply the division lemma to get
88 = 35 x 2 + 18
We consider the new divisor 35 and the new remainder 18,and apply the division lemma to get
35 = 18 x 1 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 299 and 510 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(35,18) = HCF(88,35) = HCF(211,88) = HCF(299,211) = HCF(510,299) .
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 299, 510?
Answer: HCF of 299, 510 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 299, 510 using Euclid's Algorithm?
Answer: For arbitrary numbers 299, 510 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.