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Primes look simple until a test asks whether 91 is prime, or whether 56 and 63 share a factor. Most wrong answers come from guessing by eye instead of using a method. This post explains what Chapter 5 of NCERT's new Class 6 book teaches, works each idea through with numbers, and finishes with a week of practice.
What does the Prime Time chapter cover?
Chapter 5 of Ganita Prakash, NCERT's Class 6 mathematics book (first edition August 2024, Reprint 2026-27), has six sections:
Common multiples and common factors, starting with the "idli-vada" game
Prime numbers and the Sieve of Eratosthenes
Co-prime numbers
Prime factorisation
Divisibility tests
Fun with numbers
Note what the chapter does not include. It gives quick tests for 2, 4, 5, 8 and 10, and says tests for 3, 6, 7 and 9 will come in later classes. If a guide book teaches all of them now, it may be ahead of your syllabus.
What makes a number prime?
The book begins with figs. Guna can arrange 12 figs in several rectangles (1 × 12, 2 × 6, 3 × 4), but Anshu can arrange 7 figs only as 1 × 7. The number of rows and columns are factors.
A prime has exactly two factors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13.
A composite number has more than two factors. Examples: 4, 6, 8, 9, 10.
1 has only one factor, so it is neither prime nor composite.
Worked example 1 (the sieve up to 50). Write 1 to 50 in rows. Cross out 1. Circle 2 and cross out every later multiple of 2. Circle 3 and cross out its later multiples, then do the same for 5 and 7. What is left are the primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
That is 15 primes. Why can you stop after 7? Any composite number up to 50 has a factor no bigger than 7, because the next prime, 11, gives 11 × 11 = 121, which is already past 50. The same reasoning works up to 100, where the sieve leaves 25 primes.
How do you check whether two numbers are co-prime?
Two numbers are co-prime when their only common factor is 1. The chapter shows a tempting mistake. Anshu writes 56 = 14 × 4 and 63 = 21 × 3, sees no shared factor, and says they are co-prime. Guna writes 56 = 7 × 8 and 63 = 9 × 7 and finds 7 in both. One way of splitting a number does not show all its factors.
The reliable method is prime factorisation: keep breaking factors until only primes are left.
Worked example 2.
56 = 2 × 2 × 2 × 7
63 = 3 × 3 × 7
Both contain 7, so 56 and 63 are not co-prime.
Worked example 3.
80 = 2 × 2 × 2 × 2 × 5
63 = 3 × 3 × 7
No prime appears in both lists, so 80 and 63 are co-prime.
The book also notes a remarkable fact: every number greater than 1 has only one prime factorisation, apart from the order of the factors. 36 always comes out as two 2s and two 3s, however you start.
What are the divisibility tests in Class 6?
The chapter builds each test from patterns in multiples:
By 10: the number ends in 0.
By 5: it ends in 0 or 5.
By 2: it ends in 0, 2, 4, 6 or 8.
By 4: the number formed by the last two digits is divisible by 4.
By 8: the number formed by the last three digits is divisible by 8.
Worked example 4. Is 8536 divisible by 4? Its last two digits make 36, and 36 = 4 × 9, so yes. Is it divisible by 8? Its last three digits make 536, and 536 = 8 × 67, so yes.
Why does the last-two-digits test work? Any number can be split into hundreds plus its last two digits, and 100 = 4 × 25 is always divisible by 4. So only the last two digits decide. The same idea with 1000 = 8 × 125 explains the test for 8.
Worked example 5 (leap years). The book gives the rule: a leap year is a multiple of 4, except years divisible by 100 but not by 400. From 2024 to 2099 the leap years are 2024, 2028 and so on up to 2096. That is (2096 − 2024) ÷ 4 + 1 = 19 years. The year 2100 will not be a leap year, because it is divisible by 100 but not by 400.
Why do even adults find divisibility tricky?
In clinical interviews with trainee primary teachers, Zazkis and Campbell (1996) studied divisibility, primes, factorisation and divisibility rules. They found the trainees leaned on procedures even when they did understand the ideas. A rule you can explain, like the one for 4 above, is much harder to misuse than a rule you only remember.
Which mistakes cost the most marks?
Calling 1 a prime. It has only one factor.
Saying all primes are odd. 2 is prime and even.
Judging by the last digit for 4. 12 and 22 both end in 2, but only 12 is a multiple of 4.
Trusting one factor pair. Use prime factorisation to check co-primes.
Stopping the sieve too early. Keep going until every number is circled or crossed.
How should you practise this week?
Day 1: Make your own sieve from 1 to 100 and count the primes.
Day 2: Write the prime factorisation of 36, 60, 84, 90 and 105.
Day 3: Test five pairs for co-primes, such as 18 and 35, and 81 and 18.
Day 4: Test ten 4-digit numbers for divisibility by 4 and 8, then check with long division.
Day 5: Explain to someone at home why the test for 4 looks only at the last two digits.
If you keep choosing the wrong method, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer. Prime factorisation returns when you simplify fractions, which our post on fractions in Class 6 covers, and the chapter's puzzles connect to number play in Class 6.
Tonight, test whether 91, 97 and 119 are prime, and write down the factor you find for each composite.
