Question
Is 5 × 7 × 11 × 11 a factor of 5 × 7 × 7 × 11 × 2?
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Answer
Let a = 5 × 7 × 11 × 11
6 = 5 × 7 × 7 × 11 × 2
For a to be a factor of b, b must contain all the prime factors of a, in equal or higher powers.
But here b has only one 11 (a has two 11s), so b does not include all factors of a.
Hence, 5 × 7 × 11 × 11 is not a factor of 5 × 7 × 7 × 11 × 2.
6 = 5 × 7 × 7 × 11 × 2
For a to be a factor of b, b must contain all the prime factors of a, in equal or higher powers.
But here b has only one 11 (a has two 11s), so b does not include all factors of a.
Hence, 5 × 7 × 11 × 11 is not a factor of 5 × 7 × 7 × 11 × 2.
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