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 7032, 6660 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 7032, 6660 is 12 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 7032, 6660 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 7032, 6660 is 12.
HCF(7032, 6660) = 12
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7032, 6660 is 12.
Step 1: Since 7032 > 6660, we apply the division lemma to 7032 and 6660, to get
7032 = 6660 x 1 + 372
Step 2: Since the reminder 6660 ≠ 0, we apply division lemma to 372 and 6660, to get
6660 = 372 x 17 + 336
Step 3: We consider the new divisor 372 and the new remainder 336, and apply the division lemma to get
372 = 336 x 1 + 36
We consider the new divisor 336 and the new remainder 36,and apply the division lemma to get
336 = 36 x 9 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 7032 and 6660 is 12
Notice that 12 = HCF(36,12) = HCF(336,36) = HCF(372,336) = HCF(6660,372) = HCF(7032,6660) .
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 7032, 6660?
Answer: HCF of 7032, 6660 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7032, 6660 using Euclid's Algorithm?
Answer: For arbitrary numbers 7032, 6660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.