Highest Common Factor of 498, 390 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, 390 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 390 is 6 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, 390 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, 390 is 6.
HCF(498, 390) = 6
HCF of 498, 390 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, 390 is 6.
Highest Common Factor of 498,390 is 6
Step 1: Since 498 > 390, we apply the division lemma to 498 and 390, to get
498 = 390 x 1 + 108
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 108 and 390, to get
390 = 108 x 3 + 66
Step 3: We consider the new divisor 108 and the new remainder 66, and apply the division lemma to get
108 = 66 x 1 + 42
We consider the new divisor 66 and the new remainder 42,and apply the division lemma to get
66 = 42 x 1 + 24
We consider the new divisor 42 and the new remainder 24,and apply the division lemma to get
42 = 24 x 1 + 18
We consider the new divisor 24 and the new remainder 18,and apply the division lemma to get
24 = 18 x 1 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 498 and 390 is 6
Notice that 6 = HCF(18,6) = HCF(24,18) = HCF(42,24) = HCF(66,42) = HCF(108,66) = HCF(390,108) = HCF(498,390) .
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Frequently Asked Questions on HCF of 498, 390 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, 390?
Answer: HCF of 498, 390 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 390 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 390 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.