Factors and Multiples: math test, Grade 6 – download the PDF

1 Vocabulary and lists / 4 pts

1. List all the factors of \(40\). (1 pt)
2. Write the first five multiples of \(15\). (1 pt)
3. Is \(57\) prime or composite? Justify. (1 pt)
4. Which of these numbers are prime: \(23\), \(33\), \(43\), \(53\)? (1 pt)

2 Divisibility / 3 pts

1. Which of the numbers \(2, 3, 4, 5, 6, 9, 10\) divide \(7{,}236\)? Justify with the rules. (2 pts)
2. The number \(48\square\) has a missing last digit. Find the digit that makes it divisible by both \(3\) and \(5\). (1 pt)

3 Prime factorization / 3 pts

1. Draw a factor tree for \(180\) and write its prime factorization with exponents. (2 pts)
2. Use it to explain why \(180\) is divisible by \(12\). (1 pt)

4 GCF and LCM / 4 pts

Let the numbers be \(45\) and \(75\).

1. Find their GCF. (2 pts)
2. Find their LCM. (2 pts)

5 Distributive property / 2 pts

Rewrite \(54 + 90\) as the product of the GCF and a sum, then evaluate it.

6 Word problems / 4 pts

1. A gym teacher has \(84\) beanbags and \(108\) jump ropes. She sets up identical stations with nothing left over. What is the greatest number of stations, and what does each one contain? (2 pts)
2. The Red Line train comes every \(15\) minutes and the Blue Line every \(20\) minutes. Both are at the station at 6:00 a.m. When are they there together next? (2 pts)