Highest Common Factor of 7152, 1654 using Euclid's algorithm
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 7152, 1654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7152, 1654 is 2 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 7152, 1654 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 7152, 1654 is 2.
HCF(7152, 1654) = 2
HCF of 7152, 1654 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7152, 1654 is 2.
Highest Common Factor of 7152,1654 is 2
Step 1: Since 7152 > 1654, we apply the division lemma to 7152 and 1654, to get
7152 = 1654 x 4 + 536
Step 2: Since the reminder 1654 ≠ 0, we apply division lemma to 536 and 1654, to get
1654 = 536 x 3 + 46
Step 3: We consider the new divisor 536 and the new remainder 46, and apply the division lemma to get
536 = 46 x 11 + 30
We consider the new divisor 46 and the new remainder 30,and apply the division lemma to get
46 = 30 x 1 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7152 and 1654 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(46,30) = HCF(536,46) = HCF(1654,536) = HCF(7152,1654) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7152, 1654 using Euclid's Algorithm
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 7152, 1654?
Answer: HCF of 7152, 1654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7152, 1654 using Euclid's Algorithm?
Answer: For arbitrary numbers 7152, 1654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.