Highest Common Factor of 448, 700, 45 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, 700, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 700, 45 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, 700, 45 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, 700, 45 is 1.
HCF(448, 700, 45) = 1
HCF of 448, 700, 45 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, 700, 45 is 1.
Highest Common Factor of 448,700,45 is 1
Step 1: Since 700 > 448, we apply the division lemma to 700 and 448, to get
700 = 448 x 1 + 252
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 252 and 448, to get
448 = 252 x 1 + 196
Step 3: We consider the new divisor 252 and the new remainder 196, and apply the division lemma to get
252 = 196 x 1 + 56
We consider the new divisor 196 and the new remainder 56,and apply the division lemma to get
196 = 56 x 3 + 28
We consider the new divisor 56 and the new remainder 28,and apply the division lemma to get
56 = 28 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 448 and 700 is 28
Notice that 28 = HCF(56,28) = HCF(196,56) = HCF(252,196) = HCF(448,252) = HCF(700,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 28, we apply the division lemma to 45 and 28, to get
45 = 28 x 1 + 17
Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 17 and 28, to get
28 = 17 x 1 + 11
Step 3: We consider the new divisor 17 and the new remainder 11, and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 28 and 45 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(45,28) .
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Frequently Asked Questions on HCF of 448, 700, 45 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, 700, 45?
Answer: HCF of 448, 700, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 700, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 700, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.