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 1660, 3624 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 1660, 3624 is 4 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 1660, 3624 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 1660, 3624 is 4.
HCF(1660, 3624) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1660, 3624 is 4.
Step 1: Since 3624 > 1660, we apply the division lemma to 3624 and 1660, to get
3624 = 1660 x 2 + 304
Step 2: Since the reminder 1660 ≠ 0, we apply division lemma to 304 and 1660, to get
1660 = 304 x 5 + 140
Step 3: We consider the new divisor 304 and the new remainder 140, and apply the division lemma to get
304 = 140 x 2 + 24
We consider the new divisor 140 and the new remainder 24,and apply the division lemma to get
140 = 24 x 5 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 1660 and 3624 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(140,24) = HCF(304,140) = HCF(1660,304) = HCF(3624,1660) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 1660, 3624?
Answer: HCF of 1660, 3624 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1660, 3624 using Euclid's Algorithm?
Answer: For arbitrary numbers 1660, 3624 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.