Highest Common Factor of 338, 6170, 1500 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 338, 6170, 1500 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 6170, 1500 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 338, 6170, 1500 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 338, 6170, 1500 is 2.
HCF(338, 6170, 1500) = 2
HCF of 338, 6170, 1500 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 6170, 1500 is 2.
Highest Common Factor of 338,6170,1500 is 2
Step 1: Since 6170 > 338, we apply the division lemma to 6170 and 338, to get
6170 = 338 x 18 + 86
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 86 and 338, to get
338 = 86 x 3 + 80
Step 3: We consider the new divisor 86 and the new remainder 80, and apply the division lemma to get
86 = 80 x 1 + 6
We consider the new divisor 80 and the new remainder 6,and apply the division lemma to get
80 = 6 x 13 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma 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 338 and 6170 is 2
Notice that 2 = HCF(6,2) = HCF(80,6) = HCF(86,80) = HCF(338,86) = HCF(6170,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1500 > 2, we apply the division lemma to 1500 and 2, to get
1500 = 2 x 750 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 1500 is 2
Notice that 2 = HCF(1500,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 338, 6170, 1500 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 338, 6170, 1500?
Answer: HCF of 338, 6170, 1500 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 6170, 1500 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 6170, 1500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.