Question

How many factors of the number 28 * 36 * 54 * 105 are multiples of 120?

Answer 1

Answer:

the answer is 540 mate....

Answer 2

Given,

28 * 36 * 54 * 105

To find,

The factors of 28 * 36 * 54 * 105 that are multiples of 120.

Solution,

The factors of 28 * 36 * 54 * 105 that will be multiples of 120: 2³×3×5.

We can easily solve this problem by following the given steps.

Now, the prime factors of 120 are 2×2×2×3×5.

The factor of 120 can be written as 2³×3×5.

Now, let's solve 28 * 36 * 54 * 105 by simplifying it.

28 * 36 * 54 * 105

(7×4) × (6×6) × (6×9) × (5×21)

By further simplifying it, we get

(7×2×2) × (2×3×2×3) × (2×3×3×3) × (5×3×7)

Now, adding the powers of the numbers having the same base,

7² × 2^5 × 3^6 × 5

Taking 2³×3×5 as common,

2³×3×5 (7²×2²×3^5)

Hence, the factors of 28 * 36 * 54 * 105 that are multiples of 120: 2³×3×5.