Question

who is greatest number which divide 3026 and 5053 leaving remainders 11 and 13 respectively

Answer 1

Required Number can be given by:   HCF of (3026 - 11) and (5053 - 13) HCF of 3015 and 5040 = 15. To find HCF, we break the given numbers in their prime Factors. 3015 = 3*3*5*67 5040 = 2*2*2*2*3*3*5*7 We take common multiples in these two given numbers to get required HCF. And Common multiples are: 3*5 So, Required HCF = 15.

Answer 2

Question

Find the greatest number that will divide 3026 and 5053 leaving remainders 11 and 13 respectively ?

Step-by-step explanation:

Required number =

H.C.F of (3026 - 11) and (5053 - 13)

= H.C.F of (3015, 5040)

Now, to find the H.C.F we will break down the numbers by their Prime Factors by Factor Tree method.

3015 = 3 * 3 * 5 * 67

5040 = 2 * 2 * 2 * 2 * 3 * 3 * 5 * 7

Now, we will tale the common Prime Factors above

Common Prime factors = 3 * 3 * 5

3 * 3 * 5 = 45

This means H.C.F of 3015 and 5040 is 45