Factors and multiples activity

This activity must be presented after Prime factorization and LCM.

If possible, find a number that's 1 more than a multiple of 7, and 1 more than a multiple of 4.

If possible, find a number that's 3 more than a multiple of 5, and 8 more than a multiple of 10.

If possible, find a number that's 4 more than a multiple of 6, and 2 more than a multiple of 4.

We know that

  • When 59 is divided by 5, the remainder is 4
  • When 59 is divided by 4, the remainder is 3
  • When 59 is divided by 3, the remainder is 2
  • When 59 is divided by 2, the remainder is 1

Find the smallest number \(n\) such that

  • When \(n\) is divided by 10, the remainder is 9
  • When \(n\) is divided by 9, the remainder is 8
  • \(\ldots\)
  • When \(n\) is divided by 2, the remainder is 1
Remainders
NRICH