Highest Common Factor of 72, 40, 414 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 72, 40, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 72, 40, 414 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 72, 40, 414 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 72, 40, 414 is 2.
HCF(72, 40, 414) = 2
HCF of 72, 40, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 72, 40, 414 is 2.
Highest Common Factor of 72,40,414 is 2
Step 1: Since 72 > 40, we apply the division lemma to 72 and 40, to get
72 = 40 x 1 + 32
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 32 and 40, to get
40 = 32 x 1 + 8
Step 3: We consider the new divisor 32 and the new remainder 8, and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 72 and 40 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(72,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 8, we apply the division lemma to 414 and 8, to get
414 = 8 x 51 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: 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 8 and 414 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(414,8) .
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Frequently Asked Questions on HCF of 72, 40, 414 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 72, 40, 414?
Answer: HCF of 72, 40, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 72, 40, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 72, 40, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.