Question

find the largest number that divides 10 and14 leaving a remainder of 2​

Answer 1

Answer:

4

Step-by-step explanation:

10+2 = 12

14+2 = 16

Largest number that divides 10 and 14 leaving remainder 2 = HCF of 12 and 16.

12 = 2×2×3

16 = 2×2×2×2

HCF = 2×2 = 4

Hence, 4 is the answer.

Answer 2

Given: A number divides 10 and 14 leaving a remainder of 2​.

To find: The largest possible value of this number

Solution: To solve this problem, we need to make use of Highest Common Factor (HCF).

In order to do that, first we add the remainder to the given numbers.

10 + 2 = 12

14 + 2 = 16

Now we need to find the HCF of these two numbers to get the largest number that divides them.

Let us break down the numbers into prime factors.

12 = 2² × 3

16 = 2⁴

Hence, the HCF of 12 and 16 is 2² = 4.

Therefore, the largest number that divides 10 and 14 leaving a remainder of 2​ is 4.