Highest Common Factor of 336, 570, 104 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 336, 570, 104 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 570, 104 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 336, 570, 104 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 336, 570, 104 is 2.
HCF(336, 570, 104) = 2
HCF of 336, 570, 104 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 570, 104 is 2.
Highest Common Factor of 336,570,104 is 2
Step 1: Since 570 > 336, we apply the division lemma to 570 and 336, to get
570 = 336 x 1 + 234
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 234 and 336, to get
336 = 234 x 1 + 102
Step 3: We consider the new divisor 234 and the new remainder 102, and apply the division lemma to get
234 = 102 x 2 + 30
We consider the new divisor 102 and the new remainder 30,and apply the division lemma to get
102 = 30 x 3 + 12
We consider the new divisor 30 and the new remainder 12,and apply the division lemma to get
30 = 12 x 2 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 336 and 570 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(102,30) = HCF(234,102) = HCF(336,234) = HCF(570,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 104 > 6, we apply the division lemma to 104 and 6, to get
104 = 6 x 17 + 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 104 is 2
Notice that 2 = HCF(6,2) = HCF(104,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 336, 570, 104 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 336, 570, 104?
Answer: HCF of 336, 570, 104 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 570, 104 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 570, 104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.