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 3072, 4208 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 3072, 4208 is 16 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 3072, 4208 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 3072, 4208 is 16.
HCF(3072, 4208) = 16
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3072, 4208 is 16.
Step 1: Since 4208 > 3072, we apply the division lemma to 4208 and 3072, to get
4208 = 3072 x 1 + 1136
Step 2: Since the reminder 3072 ≠ 0, we apply division lemma to 1136 and 3072, to get
3072 = 1136 x 2 + 800
Step 3: We consider the new divisor 1136 and the new remainder 800, and apply the division lemma to get
1136 = 800 x 1 + 336
We consider the new divisor 800 and the new remainder 336,and apply the division lemma to get
800 = 336 x 2 + 128
We consider the new divisor 336 and the new remainder 128,and apply the division lemma to get
336 = 128 x 2 + 80
We consider the new divisor 128 and the new remainder 80,and apply the division lemma to get
128 = 80 x 1 + 48
We consider the new divisor 80 and the new remainder 48,and apply the division lemma to get
80 = 48 x 1 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 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 3072 and 4208 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(80,48) = HCF(128,80) = HCF(336,128) = HCF(800,336) = HCF(1136,800) = HCF(3072,1136) = HCF(4208,3072) .
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 3072, 4208?
Answer: HCF of 3072, 4208 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3072, 4208 using Euclid's Algorithm?
Answer: For arbitrary numbers 3072, 4208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.