NCERT Solutions for Class 7th Maths Chapter 3 In-text Questions — The Division Method · Factors of a Number Using Prime Factorisation
Book page 50 Updated on2026-09-19
Q1.
Can you write the prime factorisation of 105 and 30 using these two figures?
The two figures from the book: a circled number with another number written to its left, a circled number below it in the same way, and a plain number at the foot.
Answer
Collect the primes written on the left, then the prime left at the bottom.
3 | 105
5 | 35
7 105 = 3 × 5 × 7
2 | 30
3 | 15
5 30 = 2 × 3 × 5
Check: 3 × 5 × 7 = 105 ✓ and 2 × 3 × 5 = 30 ✓
Tip: the last number at the bottom is a prime, so it counts too. Forgetting it is the commonest slip in this method.
Q2.
Try finding the prime factorisation of 1200 using the method above.
Answer
Divide by the smallest prime that works, again and again.
Tip: keep dividing by 2 while the number is even, then by 3, then by 5, then by 7. Working up the primes in order means you never have to guess.
Q3.
If we had used the earlier method, our calculation would have been as follows: 1200 = 40 × 30 = 5 × 8 × 5 × 6 = … Which calculation is easier to carry out?
Answer
The division method is easier.
Earlier method
Division method
You must spot a pair of factors of 1200 yourself
You only test 2, 3, 5, 7 … in order
Several unfinished pieces to keep track of (8 and 6 still composite)
One number at a time, written in a neat column
Easy to stop too early and leave a composite factor
You stop only when a prime is reached
Finishing the earlier calculation: 1200 = 40 × 30 = 5 × 8 × 5 × 6 = 5 × (2 × 2 × 2) × 5 × (2 × 3) = 2 × 2 × 2 × 2 × 3 × 5 × 5 — the same answer, but with more bookkeeping.
Why it happens: the division method turns factorising into a fixed routine — divide, write, repeat — so there is nothing to invent at each step. The earlier method needs a fresh idea every time you meet a new composite piece.
Q4.
Consider the number 840 and its prime factorisation 2 × 2 × 2 × 3 × 5 × 7. Is 2 × 2 × 7 = 28 a factor of 840?
Answer
Yes, 28 is a factor of 840.
Reorder the prime factors so that 2 × 2 × 7 sit together (reordering does not change a product):
So 840 ÷ 28 = 30, a whole number. Hence 28 is a factor.
Why it happens: 2 × 2 × 7 uses two 2s and one 7, and 840 has three 2s and one 7 to spare. Since every prime asked for is available in 840's factorisation, the group can be pulled out and what remains is the other factor. A subpart of the prime factorisation is always a factor.
Q5.
If yes, what should it be multiplied by to get 840?
Answer
It should be multiplied by 30.
840 = (2 × 2 × 7) × (2 × 3 × 5)
The primes left over are 2, 3 and 5
2 × 3 × 5 = 30
Check: 28 × 30 = 840 ✓
Tip: the partner of a factor is simply the primes that are left behind. You never need to divide.