Highest Common Factor of 80, 304, 540, 219 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 80, 304, 540, 219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 80, 304, 540, 219 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 80, 304, 540, 219 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 80, 304, 540, 219 is 1.
HCF(80, 304, 540, 219) = 1
HCF of 80, 304, 540, 219 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 80, 304, 540, 219 is 1.
Highest Common Factor of 80,304,540,219 is 1
Step 1: Since 304 > 80, we apply the division lemma to 304 and 80, to get
304 = 80 x 3 + 64
Step 2: Since the reminder 80 ≠ 0, we apply division lemma to 64 and 80, to get
80 = 64 x 1 + 16
Step 3: We consider the new divisor 64 and the new remainder 16, and apply the division lemma to get
64 = 16 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 80 and 304 is 16
Notice that 16 = HCF(64,16) = HCF(80,64) = HCF(304,80) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 540 > 16, we apply the division lemma to 540 and 16, to get
540 = 16 x 33 + 12
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 12 and 16, to get
16 = 12 x 1 + 4
Step 3: We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 16 and 540 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(540,16) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 219 > 4, we apply the division lemma to 219 and 4, to get
219 = 4 x 54 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 219 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(219,4) .
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Frequently Asked Questions on HCF of 80, 304, 540, 219 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 80, 304, 540, 219?
Answer: HCF of 80, 304, 540, 219 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 80, 304, 540, 219 using Euclid's Algorithm?
Answer: For arbitrary numbers 80, 304, 540, 219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.