Highest Common Factor of 5925, 9660 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 5925, 9660 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 5925, 9660 is 15 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 5925, 9660 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 5925, 9660 is 15.
HCF(5925, 9660) = 15
HCF of 5925, 9660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5925, 9660 is 15.
Highest Common Factor of 5925,9660 is 15
Step 1: Since 9660 > 5925, we apply the division lemma to 9660 and 5925, to get
9660 = 5925 x 1 + 3735
Step 2: Since the reminder 5925 ≠ 0, we apply division lemma to 3735 and 5925, to get
5925 = 3735 x 1 + 2190
Step 3: We consider the new divisor 3735 and the new remainder 2190, and apply the division lemma to get
3735 = 2190 x 1 + 1545
We consider the new divisor 2190 and the new remainder 1545,and apply the division lemma to get
2190 = 1545 x 1 + 645
We consider the new divisor 1545 and the new remainder 645,and apply the division lemma to get
1545 = 645 x 2 + 255
We consider the new divisor 645 and the new remainder 255,and apply the division lemma to get
645 = 255 x 2 + 135
We consider the new divisor 255 and the new remainder 135,and apply the division lemma to get
255 = 135 x 1 + 120
We consider the new divisor 135 and the new remainder 120,and apply the division lemma to get
135 = 120 x 1 + 15
We consider the new divisor 120 and the new remainder 15,and apply the division lemma to get
120 = 15 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 5925 and 9660 is 15
Notice that 15 = HCF(120,15) = HCF(135,120) = HCF(255,135) = HCF(645,255) = HCF(1545,645) = HCF(2190,1545) = HCF(3735,2190) = HCF(5925,3735) = HCF(9660,5925) .
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Frequently Asked Questions on HCF of 5925, 9660 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 5925, 9660?
Answer: HCF of 5925, 9660 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5925, 9660 using Euclid's Algorithm?
Answer: For arbitrary numbers 5925, 9660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.