Highest Common Factor of 40, 66, 172 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 40, 66, 172 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 40, 66, 172 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 40, 66, 172 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 40, 66, 172 is 2.
HCF(40, 66, 172) = 2
HCF of 40, 66, 172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 40, 66, 172 is 2.
Highest Common Factor of 40,66,172 is 2
Step 1: Since 66 > 40, we apply the division lemma to 66 and 40, to get
66 = 40 x 1 + 26
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 26 and 40, to get
40 = 26 x 1 + 14
Step 3: We consider the new divisor 26 and the new remainder 14, and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 40 and 66 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 172 > 2, we apply the division lemma to 172 and 2, to get
172 = 2 x 86 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 172 is 2
Notice that 2 = HCF(172,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 40, 66, 172 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 40, 66, 172?
Answer: HCF of 40, 66, 172 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 40, 66, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 40, 66, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.