Highest Common Factor of 498, 888, 80 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, 888, 80 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 888, 80 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, 888, 80 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, 888, 80 is 2.
HCF(498, 888, 80) = 2
HCF of 498, 888, 80 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, 888, 80 is 2.
Highest Common Factor of 498,888,80 is 2
Step 1: Since 888 > 498, we apply the division lemma to 888 and 498, to get
888 = 498 x 1 + 390
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 390 and 498, to get
498 = 390 x 1 + 108
Step 3: We consider the new divisor 390 and the new remainder 108, and apply the division lemma to get
390 = 108 x 3 + 66
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 888 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) = HCF(888,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 80 > 6, we apply the division lemma to 80 and 6, to get
80 = 6 x 13 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 80 is 2
Notice that 2 = HCF(6,2) = HCF(80,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 498, 888, 80 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, 888, 80?
Answer: HCF of 498, 888, 80 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 888, 80 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 888, 80 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
