Highest Common Factor of 498, 365, 55 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, 365, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 498, 365, 55 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 498, 365, 55 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, 365, 55 is 1.
HCF(498, 365, 55) = 1
HCF of 498, 365, 55 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, 365, 55 is 1.
Highest Common Factor of 498,365,55 is 1
Step 1: Since 498 > 365, we apply the division lemma to 498 and 365, to get
498 = 365 x 1 + 133
Step 2: Since the reminder 365 ≠ 0, we apply division lemma to 133 and 365, to get
365 = 133 x 2 + 99
Step 3: We consider the new divisor 133 and the new remainder 99, and apply the division lemma to get
133 = 99 x 1 + 34
We consider the new divisor 99 and the new remainder 34,and apply the division lemma to get
99 = 34 x 2 + 31
We consider the new divisor 34 and the new remainder 31,and apply the division lemma to get
34 = 31 x 1 + 3
We consider the new divisor 31 and the new remainder 3,and apply the division lemma to get
31 = 3 x 10 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 498 and 365 is 1
Notice that 1 = HCF(3,1) = HCF(31,3) = HCF(34,31) = HCF(99,34) = HCF(133,99) = HCF(365,133) = HCF(498,365) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 1, we apply the division lemma to 55 and 1, to get
55 = 1 x 55 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 55 is 1
Notice that 1 = HCF(55,1) .
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, 365, 55 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, 365, 55?
Answer: HCF of 498, 365, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 498, 365, 55 using Euclid's Algorithm?
Answer: For arbitrary numbers 498, 365, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
