Highest Common Factor of 504, 2504, 5656 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 504, 2504, 5656 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 2504, 5656 is 8 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 504, 2504, 5656 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 504, 2504, 5656 is 8.
HCF(504, 2504, 5656) = 8
HCF of 504, 2504, 5656 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 2504, 5656 is 8.
Highest Common Factor of 504,2504,5656 is 8
Step 1: Since 2504 > 504, we apply the division lemma to 2504 and 504, to get
2504 = 504 x 4 + 488
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 488 and 504, to get
504 = 488 x 1 + 16
Step 3: We consider the new divisor 488 and the new remainder 16, and apply the division lemma to get
488 = 16 x 30 + 8
We consider the new divisor 16 and the new remainder 8, and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 504 and 2504 is 8
Notice that 8 = HCF(16,8) = HCF(488,16) = HCF(504,488) = HCF(2504,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5656 > 8, we apply the division lemma to 5656 and 8, to get
5656 = 8 x 707 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 5656 is 8
Notice that 8 = HCF(5656,8) .
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Frequently Asked Questions on HCF of 504, 2504, 5656 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 504, 2504, 5656?
Answer: HCF of 504, 2504, 5656 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 2504, 5656 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 2504, 5656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.