Question

Obtaine the H.C.F of 420 and 272 by using Euclid 's division algorithm and verify the same by using fundamental theorem of arithmetic .

Answer 1

Here, 420>272
∴,
420=272×1+148
272=148×1+124
148=124×1+24
124=24×5+4
24=4×6+0
Since the remainder is 0, thus the HCF is 4.
The prime factorization of 420 and 272 are:
420=2×2×3×5×7
272=2×2×2×2×17
∴, HCF=2×2=4

Answer 2

Answer:

HCF of 420 and 272 is 4

Step-by-step explanation:

Given : Numbers 420 and 272.

To find : Obtain the H.C.F of 420 and 272 by using Euclid 's division algorithm and verify the same by using fundamental theorem of arithmetic ?

Solution :

Applying Euclid 's division algorithm,

H.C.F of 420 and 272

$420 = 272\times 1 + 148$

$272 = 148\times 1 +124$

$148 = 124\times 1 +24$

$124 = 24\times 5 + 4$

$24 = 4\times 6+ 0$

Now, The remainder becomes 0.

So, HCF of 420 and 272 is 4.

Applying fundamental theorem of arithmetic for verifying,

The prime factors are

$420=2\times 2\times3\times 5\times7$

$272=2\times 2\times2\times2\times 17$

$HCF(420,272)=2\times 2$

$HCF(420,272)=4$

Therefore, HCF of 420 and 272 is 4.