Highest Common Factor of 105, 408, 508 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 105, 408, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 408, 508 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 105, 408, 508 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 105, 408, 508 is 1.
HCF(105, 408, 508) = 1
HCF of 105, 408, 508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 408, 508 is 1.
Highest Common Factor of 105,408,508 is 1
Step 1: Since 408 > 105, we apply the division lemma to 408 and 105, to get
408 = 105 x 3 + 93
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 93 and 105, to get
105 = 93 x 1 + 12
Step 3: We consider the new divisor 93 and the new remainder 12, and apply the division lemma to get
93 = 12 x 7 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 105 and 408 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(93,12) = HCF(105,93) = HCF(408,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 3, we apply the division lemma to 508 and 3, to get
508 = 3 x 169 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 508 is 1
Notice that 1 = HCF(3,1) = HCF(508,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 105, 408, 508 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 105, 408, 508?
Answer: HCF of 105, 408, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 408, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 408, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.