Highest Common Factor of 448, 617, 30 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 448, 617, 30 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 617, 30 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 448, 617, 30 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 448, 617, 30 is 1.
HCF(448, 617, 30) = 1
HCF of 448, 617, 30 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 617, 30 is 1.
Highest Common Factor of 448,617,30 is 1
Step 1: Since 617 > 448, we apply the division lemma to 617 and 448, to get
617 = 448 x 1 + 169
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 169 and 448, to get
448 = 169 x 2 + 110
Step 3: We consider the new divisor 169 and the new remainder 110, and apply the division lemma to get
169 = 110 x 1 + 59
We consider the new divisor 110 and the new remainder 59,and apply the division lemma to get
110 = 59 x 1 + 51
We consider the new divisor 59 and the new remainder 51,and apply the division lemma to get
59 = 51 x 1 + 8
We consider the new divisor 51 and the new remainder 8,and apply the division lemma to get
51 = 8 x 6 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 448 and 617 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(51,8) = HCF(59,51) = HCF(110,59) = HCF(169,110) = HCF(448,169) = HCF(617,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 1, we apply the division lemma to 30 and 1, to get
30 = 1 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 30 is 1
Notice that 1 = HCF(30,1) .
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Frequently Asked Questions on HCF of 448, 617, 30 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 448, 617, 30?
Answer: HCF of 448, 617, 30 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 617, 30 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 617, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.