First 20 multiples of 3: 3, 6, 9, ..., 60.

This is AP with a=3, d=3, n=20, l=60.

Sum = n(a+l)/2 = 20(3+60)/2 = 20×63/2 = 10×63 = 630.

100 = 2² × 5².

Sum of all divisors = (1+2+4)(1+5+25) = 7 × 31 = 217.

Sum excluding 100 = 217 - 100 = 117.

Let the number be n.

Given: n = 8k + 5 for some integer k.

When divided by 4: n = 8k + 5 = 4(2k) + 4 + 1 = 4(2k + 1) + 1.

Therefore, remainder = 1.

Prime factorization of 360: 360 = 2³ × 3² × 5.

The unique prime factors are 2, 3, and 5.

Product = 2 × 3 × 5 = 30.

Using the formula: HCF × LCM = Product of two numbers.

Therefore, 12 × LCM = 2160, so LCM = 2160 ÷ 12 = 180.

Factors of 18: 1, 2, 3, 6, 9, 18.

Factors of 27: 1, 3, 9, 27.

Common factors: 1, 3, 9.

Highest common factor = 9.

20 = 2² × 5, 30 = 2 × 3 × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60.

Using HCF × LCM = Product of two numbers: 15 × 180 = 45 × other number.

Therefore, other number = 2700 ÷ 45 = 60.

144 = 2⁴ × 3². 196 = 2² × 7².

Common prime factors: 2².

Therefore, HCF = 4.

For co-prime numbers, HCF = 1.

Using HCF × LCM = Product: 1 × 221 = Product.

Therefore, product = 221.