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 1668, 4038 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 1668, 4038 is 6 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 1668, 4038 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 1668, 4038 is 6.
HCF(1668, 4038) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1668, 4038 is 6.
Step 1: Since 4038 > 1668, we apply the division lemma to 4038 and 1668, to get
4038 = 1668 x 2 + 702
Step 2: Since the reminder 1668 ≠ 0, we apply division lemma to 702 and 1668, to get
1668 = 702 x 2 + 264
Step 3: We consider the new divisor 702 and the new remainder 264, and apply the division lemma to get
702 = 264 x 2 + 174
We consider the new divisor 264 and the new remainder 174,and apply the division lemma to get
264 = 174 x 1 + 90
We consider the new divisor 174 and the new remainder 90,and apply the division lemma to get
174 = 90 x 1 + 84
We consider the new divisor 90 and the new remainder 84,and apply the division lemma to get
90 = 84 x 1 + 6
We consider the new divisor 84 and the new remainder 6,and apply the division lemma to get
84 = 6 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 1668 and 4038 is 6
Notice that 6 = HCF(84,6) = HCF(90,84) = HCF(174,90) = HCF(264,174) = HCF(702,264) = HCF(1668,702) = HCF(4038,1668) .
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 1668, 4038?
Answer: HCF of 1668, 4038 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1668, 4038 using Euclid's Algorithm?
Answer: For arbitrary numbers 1668, 4038 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.