Question

There are 527 apple 646 pear and 748 orange. these are to be arranged in heaps containing the same number of fruits.find the greatest number of fruits possible in each heap.how many heaps are formed?

Answer 1

Solution:-

NUMBER OF APPLES=527

NUMBER OF PEARS=646

NUMBER OF ORANGES =748

FIND NUMBER OF HEAPS,GREATEST NUMBER OF FRUITS


FINDING HIGHEST COMMON FACTOR (H.C.F)


Finding H.C.F by prime factorisation

527=17× 31

646=2× 17× 19

748=2× 2× 11× 17

SO 17 HEAPS CAN BE MADE

Apple = 527/17 = 31

Pear = 646/17 = 38

Orange= 748/17 = 44

THE NUMBER OF

APPLES =31

PEARS =38

ORANGES =44

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Answer 2

apples = 527
pears = 646
oranges = 748

we will now find the HCF of 527, 646 and 748.

finding HCF of 527, 646 and 748 by division method.

527 ) 646 ( 1
- 527
------
119 ) 527 ( 4
- 476
-------
51 ) 119 ( 2
- 102
------
17 ) 51 ( 3
- 51
-----
0
now, dividing 748 by 17.
17 ) 748 ( 4
- 68
-----
68
- 68
-----
0

there will be 17 heaps in which each heap will contain the same number of Apples, same number of pears and the same number of oranges.

in each heap,
Apples = 527 / 17 = 31
Pears = 646 / 17 = 38
oranges = 748 / 17 = 44

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