Highest Common Factor of 448, 666, 33 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, 666, 33 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 666, 33 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, 666, 33 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, 666, 33 is 1.
HCF(448, 666, 33) = 1
HCF of 448, 666, 33 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, 666, 33 is 1.
Highest Common Factor of 448,666,33 is 1
Step 1: Since 666 > 448, we apply the division lemma to 666 and 448, to get
666 = 448 x 1 + 218
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 218 and 448, to get
448 = 218 x 2 + 12
Step 3: We consider the new divisor 218 and the new remainder 12, and apply the division lemma to get
218 = 12 x 18 + 2
We consider the new divisor 12 and the new remainder 2, and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 448 and 666 is 2
Notice that 2 = HCF(12,2) = HCF(218,12) = HCF(448,218) = HCF(666,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 33 > 2, we apply the division lemma to 33 and 2, to get
33 = 2 x 16 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 33 is 1
Notice that 1 = HCF(2,1) = HCF(33,2) .
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Frequently Asked Questions on HCF of 448, 666, 33 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, 666, 33?
Answer: HCF of 448, 666, 33 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 666, 33 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 666, 33 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.