How to Find the Last Digit of a Product
Only the units digits matter — ignore the rest.
Last digit of 347 × 893 = 1
How do you find the last digit of a product?
Only the units digits decide the last digit of a product, so multiply those and keep the units digit of the result. For 347 × 893, the units digits are 7 and 3, and 7 × 3 = 21, so the product ends in 1. It works because every other part of the long multiplication involves at least one tens, hundreds or higher digit, and those parts all end in 0. Carries only ever move to the left, so nothing can reach the units place except the product of the two units digits. The rule extends to longer products: for 12 × 13 × 14, the units digits give 2 × 3 = 6, then 6 × 4 = 24, so the product ends in 4. It is also a fast way to rule out a wrong answer: 347 × 893 cannot be 309872, because that ends in 2. The full product is 347 × 893 = 309871, which does end in 1.
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Column work starts at the units: 7 × 3 = 21, so the answer ends in 1.
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Carries only ever travel LEFT — no other column can reach the units place.
Your turn
Three to try in your head — tap what you get.
Last digit: 126 × 998
Last digit: 996 × 106
Last digit: 892 × 877
All 36 shortcuts: the Magic Tricks library.