Highest Common Factor of 504, 3957 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, 3957 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 3957 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 504, 3957 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, 3957 is 3.
HCF(504, 3957) = 3
HCF of 504, 3957 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, 3957 is 3.
Highest Common Factor of 504,3957 is 3
Step 1: Since 3957 > 504, we apply the division lemma to 3957 and 504, to get
3957 = 504 x 7 + 429
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 429 and 504, to get
504 = 429 x 1 + 75
Step 3: We consider the new divisor 429 and the new remainder 75, and apply the division lemma to get
429 = 75 x 5 + 54
We consider the new divisor 75 and the new remainder 54,and apply the division lemma to get
75 = 54 x 1 + 21
We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 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 504 and 3957 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(75,54) = HCF(429,75) = HCF(504,429) = HCF(3957,504) .
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Frequently Asked Questions on HCF of 504, 3957 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, 3957?
Answer: HCF of 504, 3957 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 3957 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 3957 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.