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 9724, 3792 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 9724, 3792 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 9724, 3792 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 9724, 3792 is 4.
HCF(9724, 3792) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9724, 3792 is 4.
Step 1: Since 9724 > 3792, we apply the division lemma to 9724 and 3792, to get
9724 = 3792 x 2 + 2140
Step 2: Since the reminder 3792 ≠ 0, we apply division lemma to 2140 and 3792, to get
3792 = 2140 x 1 + 1652
Step 3: We consider the new divisor 2140 and the new remainder 1652, and apply the division lemma to get
2140 = 1652 x 1 + 488
We consider the new divisor 1652 and the new remainder 488,and apply the division lemma to get
1652 = 488 x 3 + 188
We consider the new divisor 488 and the new remainder 188,and apply the division lemma to get
488 = 188 x 2 + 112
We consider the new divisor 188 and the new remainder 112,and apply the division lemma to get
188 = 112 x 1 + 76
We consider the new divisor 112 and the new remainder 76,and apply the division lemma to get
112 = 76 x 1 + 36
We consider the new divisor 76 and the new remainder 36,and apply the division lemma to get
76 = 36 x 2 + 4
We consider the new divisor 36 and the new remainder 4,and apply the division lemma to get
36 = 4 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9724 and 3792 is 4
Notice that 4 = HCF(36,4) = HCF(76,36) = HCF(112,76) = HCF(188,112) = HCF(488,188) = HCF(1652,488) = HCF(2140,1652) = HCF(3792,2140) = HCF(9724,3792) .
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 9724, 3792?
Answer: HCF of 9724, 3792 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9724, 3792 using Euclid's Algorithm?
Answer: For arbitrary numbers 9724, 3792 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.