Question

Find the number of divisors of 1420.
A.14
B.15
C.13
D.12

Answer 1

Answer is D.12
1420 contains number of terms=(3)*(2)*(2) which is equal to 12.

Answer 2

Answer:

The number of divisors of 1420 is 12 and option D is correct.

Step-by-step explanation:

1420 = 2^(2) * 5 * 71

The divisors are 1, 2, 4, 5, 71, 10, 142, 20, 284, 355, 710, 1420 - (Total 12)

Now, let's understand the process.

The prime factors of 1420 are 2, 5 and 71. Powers of 2, 5 and 71 are 2, 1 and 1 respectively.

2^2 means 1420 is divisible by 2^0 (=1), 2^1 (=2) and 2^2 (=4) [first 3 numbers of the above list}

5^1 means 1420 is divisible by 5^0 (=1) and 5^1 (= 5) [ 1 is already counted, so we have to take 5 only, 4th Number of the above list]

71^1 means 1420 is divisible by 71^0 (=1) and 71^1 (=71) [ 1 is already counted, so we have to take 71 only, 5th Number of the above list]

Now, look at the possible combination of the first 5 factors.

2*5 = 10

2*71 = 142

4*5 = 20

4*71 = 284

1420 = 2 × 2 × 5 × 71 = (2^0 + 2^1 + 2^2) × (5^0 + 5^1) × (71^0 + 71^1)

1420 contains number of terms = 3 × 2 × 2 = 12

Then, the number of factors or divisors = 12

Hence, the number of divisors of 1420 is 12 and option D is correct.

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