Highest Common Factor of 369, 987, 504 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 369, 987, 504 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 369, 987, 504 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 369, 987, 504 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 369, 987, 504 is 3.
HCF(369, 987, 504) = 3
HCF of 369, 987, 504 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 369, 987, 504 is 3.
Highest Common Factor of 369,987,504 is 3
Step 1: Since 987 > 369, we apply the division lemma to 987 and 369, to get
987 = 369 x 2 + 249
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 249 and 369, to get
369 = 249 x 1 + 120
Step 3: We consider the new divisor 249 and the new remainder 120, and apply the division lemma to get
249 = 120 x 2 + 9
We consider the new divisor 120 and the new remainder 9,and apply the division lemma to get
120 = 9 x 13 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 369 and 987 is 3
Notice that 3 = HCF(9,3) = HCF(120,9) = HCF(249,120) = HCF(369,249) = HCF(987,369) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 504 > 3, we apply the division lemma to 504 and 3, to get
504 = 3 x 168 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 504 is 3
Notice that 3 = HCF(504,3) .
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Frequently Asked Questions on HCF of 369, 987, 504 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 369, 987, 504?
Answer: HCF of 369, 987, 504 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 369, 987, 504 using Euclid's Algorithm?
Answer: For arbitrary numbers 369, 987, 504 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.