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 514, 370 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 514, 370 is 2 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 514, 370 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 514, 370 is 2.
HCF(514, 370) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 514, 370 is 2.
Step 1: Since 514 > 370, we apply the division lemma to 514 and 370, to get
514 = 370 x 1 + 144
Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 144 and 370, to get
370 = 144 x 2 + 82
Step 3: We consider the new divisor 144 and the new remainder 82, and apply the division lemma to get
144 = 82 x 1 + 62
We consider the new divisor 82 and the new remainder 62,and apply the division lemma to get
82 = 62 x 1 + 20
We consider the new divisor 62 and the new remainder 20,and apply the division lemma to get
62 = 20 x 3 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 514 and 370 is 2
Notice that 2 = HCF(20,2) = HCF(62,20) = HCF(82,62) = HCF(144,82) = HCF(370,144) = HCF(514,370) .
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 514, 370?
Answer: HCF of 514, 370 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 514, 370 using Euclid's Algorithm?
Answer: For arbitrary numbers 514, 370 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.