Ch3 Challenge Problem

When the six-digit number 3456n7 is divided by 8, the remainder is 5. List both possible values of the digit n.

Hint: What’s the nearest multiple of 8?

If two positive integers have a greatest common divisor of 1 and a least common multiple of 57,

what are the possible values of the larger of the two integers?

What is the largest multiple of 12 that can be written using each digit 0, 1, 2, , 9 exactly once?

The four-digit number A55B is divisible by 36. What is the sum of A and B?

The number A4273B is a six-digit integer in which A and B are digits, and the number is divisible by 72.

Find the value of and the value of A and B.

Find the largest factor of 2520 that is not divisible by 6.

Hint: How must the prime factorization of a divisor of 2520 be related to the prime factorization of 2520?

Hint: If a number is not a multiple of 6, then what must be true about its prime factorization?

Jack finds the product of three different prime numbers.

Is it possible for the sum of the digits of Jack’s product to be 18? Why or why not?

Hint: What do you know about a number whose digits sum to 18?

• YES

• NO

The least common multiple of 12, 15, 20, and k is 420.

What is the least possible value of the positive integer k?

Hint: How do you find the least common multiple of a group of numbers? What must be true about in order for to be 420?

For each of the following pairs of numbers, find the product of the numbers, and then find the product of the greatest common divisor and least common multiple of the numbers.

18, 24

For each of the following pairs of numbers, find the product of the numbers, and then find the product of the greatest common divisor and least common multiple of the numbers.

35, 42