How it works
This 35 multiplication chart runs from 1 × 1 to 35 × 35 = 1,225. The 35 row and column are tinted, and since 35 is 5 × 7, that row counts days 5 weeks at a time.
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1,225 squares, 410 different answers
A multiplication chart 1-35 has 1,225 squares but only 410 different answers. 60 and 120 fill 10 squares each, the most of any number here. Just 20 answers appear once, every one a square number. Count a fact and its turnaround once and 630 facts are left.
Why some 35s light 8 squares and others 2
Tap a square and every square with that answer lights up. 35 × 12 = 420 is also 14 × 30, 15 × 28 and 20 × 21, so 8 squares light. 35 × 11 = 385 splits only as 5 × 77 or 7 × 55, both off the chart, so it lights 2. From 35 × 25 on, every answer in the row lights only 2.
- To multiply by 35, multiply by 70 and halve it: 70 × 16 = 1,120, so 35 × 16 = 560.
- Answers in the 35 row end in 5, then 0, then 5 again: odd numbers times 35 end in 5, even numbers in 0.
- 1,225 is both a square number and a triangular one: 1 + 2 + 3 and on up to 49 also makes 1,225.
Questions and answers
What is a multiplication chart up to 35 used for?
Calendar sums, for one. 35 days is 5 weeks, so 35 × 2 = 70 is the days in 10 weeks and 35 × 24 = 840 the hours in 5 weeks. It also checks 2-digit work: row 23 meets column 17 at 391.
How many squares are on a multiplication chart 35?
35 rows of 35, which makes 1,225. The 12 by 12 chart covers 144 of them, so 1,081 are new. The tinted 35 row and column hold 69 squares between them, not 70, because they share the corner.
How do I divide by 35 with the chart?
Find the number in the tinted row and read the column heading above it: 595 sits under 17, so 595 ÷ 35 = 17. Every number in that row ends in 0 or 5, so one that ends in another digit will not divide evenly.