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 498, 806, 362 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 806, 362 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 498, 806, 362 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 498, 806, 362 is 2.
HCF(498, 806, 362) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 806, 362 is 2.
Step 1: Since 806 > 498, we apply the division lemma to 806 and 498, to get
806 = 498 x 1 + 308
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 308 and 498, to get
498 = 308 x 1 + 190
Step 3: We consider the new divisor 308 and the new remainder 190, and apply the division lemma to get
308 = 190 x 1 + 118
We consider the new divisor 190 and the new remainder 118,and apply the division lemma to get
190 = 118 x 1 + 72
We consider the new divisor 118 and the new remainder 72,and apply the division lemma to get
118 = 72 x 1 + 46
We consider the new divisor 72 and the new remainder 46,and apply the division lemma to get
72 = 46 x 1 + 26
We consider the new divisor 46 and the new remainder 26,and apply the division lemma to get
46 = 26 x 1 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 498 and 806 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(46,26) = HCF(72,46) = HCF(118,72) = HCF(190,118) = HCF(308,190) = HCF(498,308) = HCF(806,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 362 > 2, we apply the division lemma to 362 and 2, to get
362 = 2 x 181 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 362 is 2
Notice that 2 = HCF(362,2) .
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 498, 806, 362?
Answer: HCF of 498, 806, 362 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 806, 362 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 806, 362 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.