Show that whatever may be the integers $x$and $y$ the HCF of $13x+4y$ and $29x+9y$ is equal to HCF of $x$ and $y$
2026-04-28 11:20:23.1777375223
HCF of two integers
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Because $$\small\text{hcf}(13x+4y, 29x+9y)=\text{hcf}(13x+4y, -2(13x+4y)+29x+4y)=\text{hcf}(13x+4y, 3x+y)$$ and we have that $$13x+4y-4(3x+y)=x$$