Highest Common Factor of 324, 519, 357 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 324, 519, 357 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 324, 519, 357 is 3 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 324, 519, 357 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 324, 519, 357 is 3.
HCF(324, 519, 357) = 3
HCF of 324, 519, 357 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 324, 519, 357 is 3.
Highest Common Factor of 324,519,357 is 3
Step 1: Since 519 > 324, we apply the division lemma to 519 and 324, to get
519 = 324 x 1 + 195
Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 195 and 324, to get
324 = 195 x 1 + 129
Step 3: We consider the new divisor 195 and the new remainder 129, and apply the division lemma to get
195 = 129 x 1 + 66
We consider the new divisor 129 and the new remainder 66,and apply the division lemma to get
129 = 66 x 1 + 63
We consider the new divisor 66 and the new remainder 63,and apply the division lemma to get
66 = 63 x 1 + 3
We consider the new divisor 63 and the new remainder 3,and apply the division lemma to get
63 = 3 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 324 and 519 is 3
Notice that 3 = HCF(63,3) = HCF(66,63) = HCF(129,66) = HCF(195,129) = HCF(324,195) = HCF(519,324) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 357 > 3, we apply the division lemma to 357 and 3, to get
357 = 3 x 119 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 357 is 3
Notice that 3 = HCF(357,3) .
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Frequently Asked Questions on HCF of 324, 519, 357 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 324, 519, 357?
Answer: HCF of 324, 519, 357 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 324, 519, 357 using Euclid's Algorithm?
Answer: For arbitrary numbers 324, 519, 357 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.