6×101

6×101 is the product of the integers 6 and 101. In decimal arithmetic it equals 606, since 6×101 = 6×(100+1) = 600 + 6 = 606.

Prime factorization and divisibility: 606 = 2 × 3 × 101. The factors show that 606 is divisible by 2, 3, 6, and 101. The greatest common divisor of 6 and 101 is 1 because 101 is prime and does not share factors with 6.

Representation in different bases: In base 10 the result is 606, a palindromic number. In base b, 101 in that base equals b^2 + 1, so 6×101_b equals 6b^2 + 6.

Applications and interpretation: The expression illustrates multiplication of a two-digit coefficient by a three-digit number with a 1 in the hundreds place. It can be used to demonstrate the distributive property and basic mental arithmetic, showing how breaking numbers into tens and hundreds simplifies calculation.