Question

There are 105 teachers and 435 students at a camping trip. How many identical groups could be formed
from all the teachers and students?

Answer 1

hcf of 435 and 105 =15

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Answer 2

Given:

• There are 105 teachers ad 435 students.

To Find:

• The number of identical groups that can be formed.

Explanation:

• Identical groups means to have the same number of teachers and students in each group.

Method:

1. Place each number as a product of its prime factors.
2. Find the Highest Common Factors (HCF).

Find the prime factors of 105:

$105 = 3 \times 5 \times 7$

Find the prime factors of 435

$435 = 3 \times 5 \times 29$

Find the HCF of 105 and 435:

Finding HCF is to find the greatest number that can divide the given numbers. HCF is also known as Greatest Common Divisor.

$105 = 3 \times 5 \times 7$

$435 = 3 \times 5 \times 29$

$\text{HCF} = 3 \times 5$

$\text{HCF} = 15$

HCF = 15 means that we can place the 105 teachers and 435 students in 15 identical groups, each group having the same number of teachers and students.

Answer: 15 identical groups