A student with a blue badge chooses a factor of 30. We find all factors of 30 by expressing it as products: 1 × 30, 2 × 15, 3 × 10, and 5 × 6. Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

A student with a blue badge chooses a factor of 30. We find all factors of 30 by expressing it as products: 1 × 30, 2 × 15, 3 × 10, and 5 × 6. Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

In Class 6, students played a "Factor Hunt." Students wearing a red badge chose a factor of 20. Students wearing a blue badge chose a factor of 30. For each turn, the team choosing the larger number gets 1 point, while the opposition gets 0. How many times can they tie?

Answer: 4

Step-by-step solution

Step 1: Find the factors of 20

A student with a red badge chooses a factor of $20$ . To find all factors of $20$ , we write $20$ as products of two numbers: $1 \times 20$ , $2 \times 10$ , and $4 \times 5$ . Therefore, the factors of $20$ are $1$ , $2$ , $4$ , $5$ , $10$ , and $20$ .

Step 2: Find the factors of 30

A student with a blue badge chooses a factor of $30$ . We find all factors of $30$ by expressing it as products: $1 \times 30$ , $2 \times 15$ , $3 \times 10$ , and $5 \times 6$ . Thus, the factors of $30$ are $1$ , $2$ , $3$ , $5$ , $6$ , $10$ , $15$ , and $30$ .

Step 3: Identify the common factors for a tie

A tie occurs in a turn when both the red badge student and the blue badge student choose the exact same number. This means the chosen number must be a common factor of both $20$ and $30$ . The numbers common to both sets are $1$ , $2$ , $5$ , and $10$ .

Step 4: Count the number of possible ties

There are $4$ distinct common numbers that both players can choose to result in a tie: $1$ , $2$ , $5$ , and $10$ . Therefore, there are $4$ different values on which they can tie.

Solve your own maths question free →