Highest Common Factor of 480, 108, 353, 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 480, 108, 353, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 480, 108, 353, 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 480, 108, 353, 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 480, 108, 353, 45 is 1.
HCF(480, 108, 353, 45) = 1
HCF of 480, 108, 353, 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 480, 108, 353, 45 is 1.
Highest Common Factor of 480,108,353,45 is 1
Step 1: Since 480 > 108, we apply the division lemma to 480 and 108, to get
480 = 108 x 4 + 48
Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 48 and 108, to get
108 = 48 x 2 + 12
Step 3: We consider the new divisor 48 and the new remainder 12, and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 480 and 108 is 12
Notice that 12 = HCF(48,12) = HCF(108,48) = HCF(480,108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 353 > 12, we apply the division lemma to 353 and 12, to get
353 = 12 x 29 + 5
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get
12 = 5 x 2 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 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 12 and 353 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(353,12) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
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Frequently Asked Questions on HCF of 480, 108, 353, 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 480, 108, 353, 45?
Answer: HCF of 480, 108, 353, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 480, 108, 353, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 480, 108, 353, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.