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 755, 7015, 6166 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 755, 7015, 6166 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 755, 7015, 6166 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 755, 7015, 6166 is 1.
HCF(755, 7015, 6166) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 755, 7015, 6166 is 1.
Step 1: Since 7015 > 755, we apply the division lemma to 7015 and 755, to get
7015 = 755 x 9 + 220
Step 2: Since the reminder 755 ≠ 0, we apply division lemma to 220 and 755, to get
755 = 220 x 3 + 95
Step 3: We consider the new divisor 220 and the new remainder 95, and apply the division lemma to get
220 = 95 x 2 + 30
We consider the new divisor 95 and the new remainder 30,and apply the division lemma to get
95 = 30 x 3 + 5
We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get
30 = 5 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 755 and 7015 is 5
Notice that 5 = HCF(30,5) = HCF(95,30) = HCF(220,95) = HCF(755,220) = HCF(7015,755) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6166 > 5, we apply the division lemma to 6166 and 5, to get
6166 = 5 x 1233 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 6166 is 1
Notice that 1 = HCF(5,1) = HCF(6166,5) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 755, 7015, 6166?
Answer: HCF of 755, 7015, 6166 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 755, 7015, 6166 using Euclid's Algorithm?
Answer: For arbitrary numbers 755, 7015, 6166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.