Highest Common Factor of 1516, 9942 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 1516, 9942 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1516, 9942 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 1516, 9942 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 1516, 9942 is 2.
HCF(1516, 9942) = 2
HCF of 1516, 9942 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1516, 9942 is 2.
Highest Common Factor of 1516,9942 is 2
Step 1: Since 9942 > 1516, we apply the division lemma to 9942 and 1516, to get
9942 = 1516 x 6 + 846
Step 2: Since the reminder 1516 ≠ 0, we apply division lemma to 846 and 1516, to get
1516 = 846 x 1 + 670
Step 3: We consider the new divisor 846 and the new remainder 670, and apply the division lemma to get
846 = 670 x 1 + 176
We consider the new divisor 670 and the new remainder 176,and apply the division lemma to get
670 = 176 x 3 + 142
We consider the new divisor 176 and the new remainder 142,and apply the division lemma to get
176 = 142 x 1 + 34
We consider the new divisor 142 and the new remainder 34,and apply the division lemma to get
142 = 34 x 4 + 6
We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get
34 = 6 x 5 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1516 and 9942 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(142,34) = HCF(176,142) = HCF(670,176) = HCF(846,670) = HCF(1516,846) = HCF(9942,1516) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 1516, 9942 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 1516, 9942?
Answer: HCF of 1516, 9942 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1516, 9942 using Euclid's Algorithm?
Answer: For arbitrary numbers 1516, 9942 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.