Highest Common Factor of 498, 300, 214 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 498, 300, 214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 300, 214 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, 300, 214 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, 300, 214 is 2.
HCF(498, 300, 214) = 2
HCF of 498, 300, 214 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 498, 300, 214 is 2.
Highest Common Factor of 498,300,214 is 2
Step 1: Since 498 > 300, we apply the division lemma to 498 and 300, to get
498 = 300 x 1 + 198
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 198 and 300, to get
300 = 198 x 1 + 102
Step 3: We consider the new divisor 198 and the new remainder 102, and apply the division lemma to get
198 = 102 x 1 + 96
We consider the new divisor 102 and the new remainder 96,and apply the division lemma to get
102 = 96 x 1 + 6
We consider the new divisor 96 and the new remainder 6,and apply the division lemma to get
96 = 6 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 498 and 300 is 6
Notice that 6 = HCF(96,6) = HCF(102,96) = HCF(198,102) = HCF(300,198) = HCF(498,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 214 > 6, we apply the division lemma to 214 and 6, to get
214 = 6 x 35 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 214 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(214,6) .
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Frequently Asked Questions on HCF of 498, 300, 214 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 498, 300, 214?
Answer: HCF of 498, 300, 214 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 300, 214 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 300, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.