Highest Common Factor of 448, 1410, 1914 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, 1410, 1914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 1410, 1914 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 448, 1410, 1914 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, 1410, 1914 is 2.
HCF(448, 1410, 1914) = 2
HCF of 448, 1410, 1914 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, 1410, 1914 is 2.
Highest Common Factor of 448,1410,1914 is 2
Step 1: Since 1410 > 448, we apply the division lemma to 1410 and 448, to get
1410 = 448 x 3 + 66
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 66 and 448, to get
448 = 66 x 6 + 52
Step 3: We consider the new divisor 66 and the new remainder 52, and apply the division lemma to get
66 = 52 x 1 + 14
We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get
52 = 14 x 3 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 448 and 1410 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(66,52) = HCF(448,66) = HCF(1410,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1914 > 2, we apply the division lemma to 1914 and 2, to get
1914 = 2 x 957 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 1914 is 2
Notice that 2 = HCF(1914,2) .
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Frequently Asked Questions on HCF of 448, 1410, 1914 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, 1410, 1914?
Answer: HCF of 448, 1410, 1914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 1410, 1914 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 1410, 1914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.