Bigest divider...?

1 ⤊

The product of two natural numbers is 8400, and their biggest divider is 20, which are the two numbers?

2007-11-21 03:31:08 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

No1 = HCF × UCF1 -------- un common factor 1
No2 = HCF × UCF2 -------- un common factor 2
No1 × No2 = HCF × HCF × UCF1 × UCF2
UCF1 × UCF2 = 8400 / 20 × 20 = 21
21 = 1 × 21 = 3 × 7
No 1 = 20 × 1 = 20
No2 = 20 × 21 = 420
And another pair
No 1 = 20 × 3 = 60
No2 = 20 × 7 = 140
So numbers are 20, 420 or 60, 140

2007-11-21 03:51:51 · answer #1 · answered by Pranil 7 · 1⤊ 0⤋

xy = 8400
both x and y are divisible by 20
x/20 * y/20 = 8400 / (20*20) = 21

factors of 21 are 3, 7
so x, y = 60, 140 in some order

2007-11-21 11:40:24 · answer #2 · answered by Steve A 7 · 0⤊ 0⤋