Highest Common Factor of 510, 298, 733 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 510, 298, 733 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 298, 733 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 510, 298, 733 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 510, 298, 733 is 1.
HCF(510, 298, 733) = 1
HCF of 510, 298, 733 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 298, 733 is 1.
Highest Common Factor of 510,298,733 is 1
Step 1: Since 510 > 298, we apply the division lemma to 510 and 298, to get
510 = 298 x 1 + 212
Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 212 and 298, to get
298 = 212 x 1 + 86
Step 3: We consider the new divisor 212 and the new remainder 86, and apply the division lemma to get
212 = 86 x 2 + 40
We consider the new divisor 86 and the new remainder 40,and apply the division lemma to get
86 = 40 x 2 + 6
We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get
40 = 6 x 6 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 510 and 298 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(86,40) = HCF(212,86) = HCF(298,212) = HCF(510,298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 733 > 2, we apply the division lemma to 733 and 2, to get
733 = 2 x 366 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 733 is 1
Notice that 1 = HCF(2,1) = HCF(733,2) .
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Frequently Asked Questions on HCF of 510, 298, 733 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 510, 298, 733?
Answer: HCF of 510, 298, 733 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 298, 733 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 298, 733 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.