Highest Common Factor of 166, 126, 749 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 166, 126, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 166, 126, 749 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 166, 126, 749 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 166, 126, 749 is 1.
HCF(166, 126, 749) = 1
HCF of 166, 126, 749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 166, 126, 749 is 1.
Highest Common Factor of 166,126,749 is 1
Step 1: Since 166 > 126, we apply the division lemma to 166 and 126, to get
166 = 126 x 1 + 40
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 40 and 126, to get
126 = 40 x 3 + 6
Step 3: We consider the new divisor 40 and the new remainder 6, and apply the division lemma to get
40 = 6 x 6 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 166 and 126 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(126,40) = HCF(166,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 2, we apply the division lemma to 749 and 2, to get
749 = 2 x 374 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 749 is 1
Notice that 1 = HCF(2,1) = HCF(749,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 166, 126, 749 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 166, 126, 749?
Answer: HCF of 166, 126, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 166, 126, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 166, 126, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.