A) express 4116 as the product of its prime factors. b) find the hcf and lcm of 4116 and 2 ×3⁴× 7² × 11​

Step-by-step explanation:

(a) We need to express 4116 as the product of its prime factors.

Prime factors of 4116 = 2 x 2 x 3 x 7 x 7 x 7

or

= 2² x 3¹ x 7³

(b) HCF of 4116 and 2 ×3⁴× 7² × 11​.

4116 = 2² x 3¹ x 7³

2 ×3⁴× 7² × 11​

Factors of 4116 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 343, 588, 686, 1029, 1372, 2058, 4116

Factors of 2 ×3⁴× 7² × 11​ = 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 27, 33, 42, 49, 54, 63, 66, 77, 81, 98, 99, 126, 147, 154, 162, 189, 198, 231, 294, 297, 378, 441, 462, 539, 567, 594, 693, 882, 891, 1078, 1134, 1323, 1386, 1617, 1782, 2079, 2646, 3234, 3969, 4158, 4851, 6237, 7938, 9702, 12474, 14553, 29106, 43659, 87318

HCF = 294

LCM of 4116 and 2 ×3⁴× 7² × 11​ = 1,222,452

Hence, this is the required solution.

salary

step-by-step explanation: