The number 3 power 13 - 3 to the power 10 is divisible by what
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3¹³ - 3¹⁰ is always Divisible by 2, 3 and 13
Step-by-step explanation:
3¹³ - 3¹⁰
= 3⁽¹⁰⁺³⁾ - 3¹⁰
= 3¹⁰ * 3³ - 3¹⁰
= 3¹⁰ ( 3³ - 1)
= 3¹⁰ ( 27 - 1)
= 3¹⁰ * 26
26 = 2 * 13
only factors are 2 , 3 , 13
so not divisible by 10
3¹³ - 3¹⁰ is always Divisible by 26
as 3¹³ - 3¹⁰ is divisible by 2 , 3 , 6 , 9 , 13 , 18 , 26 , 27 , 39 , 54 , 78
from option 2 , 3 & 13 is correct answer
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