Highest Common Factor of 172, 406, 744 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 172, 406, 744 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 406, 744 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 172, 406, 744 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 172, 406, 744 is 2.
HCF(172, 406, 744) = 2
HCF of 172, 406, 744 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 172, 406, 744 is 2.
Highest Common Factor of 172,406,744 is 2
Step 1: Since 406 > 172, we apply the division lemma to 406 and 172, to get
406 = 172 x 2 + 62
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 62 and 172, to get
172 = 62 x 2 + 48
Step 3: We consider the new divisor 62 and the new remainder 48, and apply the division lemma to get
62 = 48 x 1 + 14
We consider the new divisor 48 and the new remainder 14,and apply the division lemma to get
48 = 14 x 3 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 172 and 406 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(48,14) = HCF(62,48) = HCF(172,62) = HCF(406,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 744 > 2, we apply the division lemma to 744 and 2, to get
744 = 2 x 372 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 744 is 2
Notice that 2 = HCF(744,2) .
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Frequently Asked Questions on HCF of 172, 406, 744 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 172, 406, 744?
Answer: HCF of 172, 406, 744 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 406, 744 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 406, 744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.