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Math

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PROBLEM

5. If 21 divides mm, what else must divide mm ?

STEP 1

1. The integer m m is divisible by 21 21 .
2. We need to determine other divisors of m m based on its divisibility by 21 21 .

STEP 2

1. Factorize 21.
2. Identify divisors of 21.
3. Conclude divisors of m m .

STEP 3

Factorize 21 21 into its prime factors.
21=3×7 21 = 3 \times 7

STEP 4

Identify all divisors of 21 21 using its prime factorization.
The divisors of 21 21 are 1,3,7, 1, 3, 7, and 21 21 .

SOLUTION

Conclude that if 21 21 divides m m , then all divisors of 21 21 must also divide m m .
Therefore, m m must be divisible by 1,3,7, 1, 3, 7, and 21 21 .
The divisors of m m must include:
1,3,7, and 21\boxed{1, 3, 7, \text{ and } 21}

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