Explanation

To convert 45 to binary:

45 ÷ 2 = 22 remainder 1

22 ÷ 2 = 11 remainder 0

11 ÷ 2 = 5 remainder 1

5 ÷ 2 = 2 remainder 1

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

Reading remainders from bottom to top: 101101

Therefore, 45 in binary = 101101.

Explanation

7 + 1 = 8

8 + 2 = 10

10 + 4 = 14

14 + 8 = 22

22 + 16 = 38

Explanation

The greatest six-digit number is 999999 (all digits are 9).

Any higher number becomes a seven-digit number (starts from 1000000).

Explanation

The given equation (a + b) + c = a + (b + c) is the standard form of the Associative Property of Addition.

It states that the grouping of numbers in an addition operation does not change the sum.

Explanation

The associative property of the union states that:

A ∪ (B ∪ C) = (A ∪ B) ∪ C

This means that the order in which we perform the union operation does not change the result.

Explanation

3 × 10¹ = 3 × 10 = 30.

4 × 10⁰ = 4 × 1 = 4.

30 + 4 = 34.

Explanation

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Factors of 28: 1, 2, 4, 7, 14, 28

Common factors: 1, 2, 7, 14 → Highest is 14

So, HCF = 14.

Explanation

Explanation

2 is the smallest and the only even prime number.

A prime number has exactly two distinct factors: 1 and itself; 1 does not meet this condition.

Explanation

Pythagoras was an ancient Greek mathematician and philosopher.

He is famous for the Pythagorean Theorem, which relates to right-angled triangles.