In Division and Factors we saw that
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho2fKNzv774Fr6lqkc5gOUiZl3wy0HiyqjhiACIGLYpSzPywOQQeE8l1AwJAK52cOBMGT-cihZvgsMwgoUZzZf77HgR66cZmDvm7x65hI5YEakCaXyD-awKtM6PmvziZFjfgB4r_7nDmsX/s1600/image019.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy09yoF5V6znT-glDsoPZHNWTZo1a43eUYPL6ZhPsK0xHSCTLLfzM5Kuk0WEFvDBGvJzX0kCgl7byoTsjMKEhY566Lhhy0x_f9KlOO-xHZxKRhXSCku8cHZ9TS-8CydjM9f-hppf9UfyLY/s1600/image021.png)
The higher the common factor the smaller are the numbers left to divide.
A puzzle is to find the highest possible common factor to the two numbers.
The solution is to split the two numbers into prime factors and list those they have in common.
For example finding the HCF of 54 and 18
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisVNPttO850WxOu1V2HqIlKohRjbyhq5BBqzdjdKOsEPhouScNXTgu_TKHGzz8EGGlJzwP2_WnQrLkLV0cZ5Ic0jTSTuV65PH-Q8vLBFNJ7-bid9G0h9wD9ociwifWmPmI9vsYIIsxYRsA/s1600/image001.jpg)
If necessary rearrange the order of the prime factor cards and pair the factors that belong to each number
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxHzHm3YkTLfJ7i-4M4C4fLfktlKLMFAMzjgEVIiCtOhlO-vjAY3iO7w0Eieme2ZS2VcpAOilw8RrRhxQKeuaaIx8Z87lgOc5LcK5FiKeTzdPffAS8toPXK9J8b8YiG6Bgf862FK0oxRjL/s1600/image003.jpg)
Multiply the common factors
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM3UQzjWop4G77P9Hy5dm4nQPBTvLjWphgNPdsVH47K_OjXZu-QihVY6B79VTg5mlMuBGbR7kLR-d_zajUIcE93LCu1oqcxQATwRw7tDbFCQ2Rbug1sytsUYQHdyPaw1cNTmfFEb31zFkQ/s1600/image005.jpg)
to find the product of these numbers
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOl3MGb9yfUqC7exVJSQhn5SR6n_vFmbQU78Qm1K68cBppGBG7JI_WjR1U086YjzgSgtmtUqJS63YnCj0KbFTgu9JnHFRIlYBaKFspTs8lnandrofsbWZNeb4rmtD_IdLh1uGezZ3V5JgQ/s1600/image007.jpg)
Eighteen is the Highest Common Factor (HCF) of Fifty Four and Eighteen.
54 = 18 x 3
18 = 18 x 1
Using Eighteen as the highest common factor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEIAuBw-IkHssNDiz01-oEwN6HCDSVc-UZef_ZaaIxBAv4KU4A679pPRu2bZH-XJOMEkaaPB-FCxkg9QBWRDPlVneyMLSDCM73niZlSj8rd1WUc1RvwN5FoQj8mIbSspqDDWD3KYMGoLFD/s1600/image002.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq6mAhD7qb07VzIy6OGgzPl2tsbodD1JxApAC95Yc_MmPVH5jaWNDm5LQTh3C9UQWVIFY-MCJyiQ-qzylaWNE2dtmQtKipxZwhQkJw4p2oX-zYqtSjdBnJ87_em020opDL9Vg_vJa5aVCC/s1600/image004.png)
which gives the same results as
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBzgUjec3guJXpoVtjvjU6xX1EJFH-AG7hQZaddCR3j3qr2ofxdl00c1I6WCAgLAvYZhvnq1ZldSz5k4Sw0S18GcCpf8wXSRd9BWmKRjgzouOTC53qMkiFNYzJMWui-jmJECsDQz84yoHz/s1600/image006.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-oQaI4iKMLmiypyjWPuY_UJbY24dCb9tmWmPzQtiTMXw248t7PSVztgLdzlMgya6fCOWU2CvR3q9CnaJTNwdk3rfShm-ieyBLLsIS6Hunt1bsH3g2J0SNRwxjF1j2BfK7_9tSnsLYmmKm/s1600/image008.png)
Record |
Maths![]() |
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