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 640, 5872, 4092 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 5872, 4092 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 640, 5872, 4092 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 640, 5872, 4092 is 4.
HCF(640, 5872, 4092) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 5872, 4092 is 4.
Step 1: Since 5872 > 640, we apply the division lemma to 5872 and 640, to get
5872 = 640 x 9 + 112
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 112 and 640, to get
640 = 112 x 5 + 80
Step 3: We consider the new divisor 112 and the new remainder 80, and apply the division lemma to get
112 = 80 x 1 + 32
We consider the new divisor 80 and the new remainder 32,and apply the division lemma to get
80 = 32 x 2 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 640 and 5872 is 16
Notice that 16 = HCF(32,16) = HCF(80,32) = HCF(112,80) = HCF(640,112) = HCF(5872,640) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4092 > 16, we apply the division lemma to 4092 and 16, to get
4092 = 16 x 255 + 12
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 12 and 16, to get
16 = 12 x 1 + 4
Step 3: We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 16 and 4092 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(4092,16) .
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 640, 5872, 4092?
Answer: HCF of 640, 5872, 4092 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 5872, 4092 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 5872, 4092 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.