Highest Common Factor of 104, 260, 608 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 104, 260, 608 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 104, 260, 608 is 4 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 104, 260, 608 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 104, 260, 608 is 4.
HCF(104, 260, 608) = 4
HCF of 104, 260, 608 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 104, 260, 608 is 4.
Highest Common Factor of 104,260,608 is 4
Step 1: Since 260 > 104, we apply the division lemma to 260 and 104, to get
260 = 104 x 2 + 52
Step 2: Since the reminder 104 ≠ 0, we apply division lemma to 52 and 104, to get
104 = 52 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 104 and 260 is 52
Notice that 52 = HCF(104,52) = HCF(260,104) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 608 > 52, we apply the division lemma to 608 and 52, to get
608 = 52 x 11 + 36
Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 36 and 52, to get
52 = 36 x 1 + 16
Step 3: We consider the new divisor 36 and the new remainder 16, and apply the division lemma to get
36 = 16 x 2 + 4
We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 52 and 608 is 4
Notice that 4 = HCF(16,4) = HCF(36,16) = HCF(52,36) = HCF(608,52) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 104, 260, 608 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 104, 260, 608?
Answer: HCF of 104, 260, 608 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 104, 260, 608 using Euclid's Algorithm?
Answer: For arbitrary numbers 104, 260, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.