Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Which of the following numbers is divisible by both 17 and 13?
22372
21401
21658
20049
21658
To determine if a number is divisible by both 17 and 13, it must be divisible by their least common multiple (LCM), which is 221 since 17 and 13 are co-prime numbers. Dividing 21658 by 221 yields a quotient of 98 with no remainder, confirming its divisibility by both.
To determine if a number is divisible by both 17 and 13, it must be divisible by their least common multiple (LCM), which is 221 since 17 and 13 are co-prime numbers. Dividing 21658 by 221 yields a quotient of 98 with no remainder, confirming its divisibility by both.
Divisibility rules in mathematics represent foundational numerical properties akin to the 'Basic Structure' doctrine in the Indian Constitution, which serves as the anchor for all legal interpretations.
Numbers 13 and 17 are both prime numbers, meaning they have no common factors other than 1.
The rule of co-primes states that if a number is divisible by two co-prime numbers a and b, it must be divisible by their product (a multiplied by b).
Applying the divisibility test for 221 (13 x 17) is the most efficient way to solve this in competitive exams.
21658 / 13 = 1666
21658 / 17 = 1274
22372 is not divisible by 221 (22372 / 221 equals approximately 101.23).
21401 is not divisible by 221 (21401 / 221 equals approximately 96.83).
C is correct тАФ 21658 is exactly divisible by 221, the product of the primes 13 and 17.
Mastering divisibility tests for primes (like 7, 11, 13, 17) significantly improves speed in Data Interpretation (DI) sections of competitive exams, where percentage calculations often involve these divisors.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants